Exhibit 10.13

EXECUTION

CONSENT TO THE

FIFTH AMENDED AND RESTATED CREDIT AGREEMENT

This CONSENT TO THE FIFTH AMENDED AND RESTATED CREDIT AGREEMENT (this “Consent”) dated as of December 29, 2014 is by and among (a) CENTURY EXPLORATION NEW ORLEANS, LLC, a Delaware limited liability company (“CNO”), CENTURY EXPLORATION HOUSTON, LLC, a Delaware limited liability company (“CEH”), and CENTURY EXPLORATION RESOURCES, LLC, a Delaware limited liability company (“CER”, and collectively with CNO and CEH, (the “Borrowers”), as borrowers, (b) RAAM GLOBAL ENERGY COMPANY, a Delaware corporation (“RAAM”, and collectively with the Borrowers, the “Loan Parties”), as guarantor, (c) the Lenders set forth on the signature pages hereto and (d) WILMINGTON TRUST, NATIONAL ASSOCIATION, as Administrative Agent for the Secured Parties (the “Administrative Agent”).

RECITALS:

WHEREAS, the Loan Parties, the Lenders from time to time party thereto and the Administrative Agent are parties to that certain Fifth Amended and Restated Credit Agreement, dated as of September 12, 2014 (as amended, restated, amended and restated, supplemented or otherwise modified from time to time prior to the date hereof, the “Credit Agreement” and as modified by this Consent, the “Modified Credit Agreement”);

WHEREAS, on December 22, 2014, the Loan Parties purchased notes issued under the Second Lien Indenture having an aggregate principal amount of $12,000,000 at a price equal to the sum of (i) 43.5% of such aggregate principal amount and (ii) accrued interest on such principal amount, for a total purchase price of $5,574,166.67 (the “Specified Second Lien Repurchase”), which such Specified Second Lien Repurchase is not permitted under the terms of the Credit Agreement;

WHEREAS, the Loan Parties have requested that the Majority Lenders (a) consent to the Specified Second Lien Repurchase and (b) consent to the release of the security interest held by the Administrative Agent for the benefit of the Secured Parties in the $5,574,166.67 of Cash used by the Loan Parties to consummate the Specified Second Lien Repurchase (the “Specified Collateral”); and

WHEREAS, the Administrative Agent, the Lenders and Loan Parties are entering into this Consent to reflect the written consent of the Administrative Agent and the Lenders party hereto, which constitute at least the Majority Lenders, to the Specified Second Lien Repurchase and to the release of the security interest in the Specified Collateral held by the Administrative Agent for the benefit of the Secured Parties, in each case, subject to conditions set forth herein.

NOW, THEREFORE, in consideration of the premises and the agreements, provisions and covenants herein contained, the parties hereto agree as follows:

Section 1. Defined Terms. Except as otherwise defined in this Consent, capitalized terms defined in the Modified Credit Agreement and used herein shall have the meanings given to them in the Modified Credit Agreement. As used in this Consent, the following terms shall have the meaning given to such terms in this Section 1:

Consent to the Fifth Amended and Restated Credit Agreement

“Additional Amount Payment Letter” shall mean that certain Additional Amount Payment Letter dated as of the date hereof by and among the Loan Parties, the Administrative Agent and the Majority Lenders.

“Specified Collateral” shall have the meaning assigned to such term in the Recitals hereto.

“Specified Second Lien Repurchase” shall have the meaning assigned to such term in the Recitals hereto.

Section 2. Consent and Release. Effective as of December 22, 2014, subject to satisfaction of the conditions precedent in Section 3 below, the Administrative Agent and Lenders party hereto hereby (a) consent to the Specified Second Lien Repurchase and (b) consent to the release of the Specified Collateral from the security interest held by the Administrative Agent for the benefit of the Secured Parties. For the avoidance of doubt, other than the Specified Second Lien Repurchase, this Section 2 does not constitute a waiver from or consent by the Administrative Agent or any Lender for any other past, current or future repayment, prepayment, redemption or other repurchase made by any Loan Party of (or or on account of) any Indebtedness outstanding under the Second Lien Indenture not permitted under the Credit Agreement. For the avoidance of doubt, other than the Specified Collateral, no other Collateral is hereby released, and this Section 2 does not constitute consent by the Administrative Agent or any Lender for any future release. The consent set forth in this Section 2 is a limited consent and the release set forth in this Section 2 is a limited release. The Loan Parties hereby agree that such consent and release do not constitute a waiver of the Administrative Agent’s or any Lender’s right to insist upon strict compliance with each term, covenant, condition and provision of the Credit Agreement and the other Loan Documents in accordance with the terms thereof.

Section 3. Effectiveness. The effectiveness of the consent and release set forth in Section 2 of this Consent is subject to the satisfaction of the following conditions precedent as determined in the Majority Lender’s sole discretion (the date of such satisfaction, the “Consent Effective Date”):

(a) the Loan Parties, the Administrative Agent and the Majority Lenders shall have executed and delivered counterparts of this Consent to the Administrative Agent;

(b) the Loan Parties, the Administrative Agent and the Majority Lenders shall have executed and delivered counterparts of the Additional Amount Payment Letter to the Administrative Agent;

(c) each of the representations and warranties contained in Section 5 of this Consent shall be true and correct in all material respects on and as of the Consent Effective Date with the same effect as though made on and as of such date, except to the extent any such representations or warranties contain qualifiers such as “material”, “in all material respects,” “except as could not reasonably be expected to result in, either individually or in the aggregate, a Material Adverse Change” or similar qualifying language or similar qualifiers, in which case such representations or warranties shall be true and correct in all respects as of such date, unless

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Consent to the Fifth Amended and Restated Credit Agreement

such representations and warranties expressly relate to an earlier date (in which case such representations and warranties shall be true and correct in all material respects on and as of such earlier date, except to the extent any such representations or warranties contain qualifiers such as “material”, “in all material respects,” “except as could not reasonably be expected to result in, either individually or in the aggregate, a Material Adverse Change” or similar qualifying language or similar qualifiers, in which case such representations or warranties shall be true and correct in all respects as of such earlier date);

(d) at the time of and immediately after giving effect to the transactions contemplated by this Consent, no Default or Event of Default shall have occurred and be continuing; and

(e) the Borrowers shall have paid to the Administrative Agent all fees, payments and expenses that are due and payable on or before the Consent Effective Date, including, without limitation, pursuant to Section 4 below, Section 10.4 of the Modified Credit Agreement and Section 1 of the Additional Amount Payment Letter.

Section 4. Costs and Expenses. Without limiting the obligations of the Borrowers under the Modified Credit Agreement, the Borrowers hereby jointly and severally agree to pay or reimburse all of the Administrative Agent’s and each Lender’s reasonable costs and expenses incurred in connection with the preparation, negotiation and execution of this Consent and the other instruments, agreements and documents to be delivered in connection herewith or therewith in accordance with the terms of Section 10.4 of the Modified Credit Agreement, including all reasonable fees, disbursements and other charges of Kirkland & Ellis LLP, counsel for the Majority Lenders.

Section 5. Representations and Warranties. Each Loan Party hereby represents and warrants, on and as of the Consent Effective Date, that:

(a) Each of the representations and warranties made by any Loan Party set forth in Section 5 of the Credit Agreement or in any other Loan Document shall be true and correct in all material respects on and as of the Consent Effective Date with the same effect as though made on and as of such date, except to the extent any such representations or warranties contain qualifiers such as “material”, “in all material respects,” “except as could not reasonably be expected to result in, either individually or in the aggregate, a Material Adverse Change” or similar qualifying language or similar qualifiers, in which case such representations or warranties shall be true and correct in all respects as of such date, unless such representations and warranties expressly relate to an earlier date (in which case such representations and warranties shall be true and correct in all material respects on and as of such earlier date, except to the extent any such representations or warranties contain qualifiers such as “material”, “in all material respects,” “except as could not reasonably be expected to result in, either individually or in the aggregate, a Material Adverse Change” or similar qualifying language or similar qualifiers, in which case such representations or warranties shall be true and correct in all respects as of such earlier date).

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Consent to the Fifth Amended and Restated Credit Agreement

(b) Each Loan Party has duly taken all action necessary to authorize the execution and delivery by it of this Consent and the Additional Amount Payment Letter and to authorize the consummation of the transactions contemplated hereby and thereby and the performance of its obligations hereunder and thereunder.

(c) The execution and delivery by each Loan Party of this Consent and the Additional Amount Payment Letter, the performance by such Loan Party of its obligations hereunder and under the Additional Amount Payment Letter, the Modified Credit Agreement and the other Loan Documents to which it is a party and the consummation of the transactions contemplated hereby and thereby, do not (a) conflict with, violate or result in a breach of, any provision of (i) any Law, (ii) the organizational documents of such Loan Party, or (iii) any material agreement, judgment, license, order or permit applicable to or binding upon such Loan Party, (b) result in the acceleration of any Indebtedness owed by any Loan Party, or (c) result in or require the creation of any Lien upon any assets or properties of any Loan Party except as expressly contemplated or permitted in the Loan Documents.

(d) Except (i) as expressly contemplated in the other Loan Documents and (ii) such as have been obtained or made and are in full force and effect, the execution, delivery and performance of this Consent, the Additional Amount Payment Letter, the Modified Credit Agreement and the other Loan Documents do not require any permit, consent, approval, authorization or order of, and no notice to or filing with, any Tribunal or third party is required in connection with the execution, delivery or performance by any Loan Party or any of its respective Subsidiaries of any Loan Document or to consummate any transactions contemplated by the Loan Documents.

(e) This Consent, the Additional Amount Payment Letter and the other Loan Documents when duly executed and delivered will be, legal, valid and binding obligations of each Loan Party and each of its respective Subsidiaries to the extent it is a party hereto or thereto, enforceable against such Loan Party or Subsidiary in accordance with their terms except as such enforcement may be limited by bankruptcy, insolvency or similar Laws of general application relating to the enforcement of creditors’ rights.

(f) After giving effect to Section 2, no Loan Party nor any of its Subsidiaries is in default in the performance of any of its covenants and agreements contained in any Loan Document. After giving effect to Section 2, no event has occurred and is continuing that constitutes a Default or an Event of Default.

(g) Upon giving effect to the execution and delivery of this Consent and the Additional Amount Payment Letter and the consummation of the transactions contemplated hereby and thereby, no Borrower or Guarantor will be Insolvent.

Section 6. Reference to and Effect on the Credit Agreement.

(a) On and after the effectiveness of this Consent, each reference in the Credit Agreement to “this Agreement,” “hereunder,” “hereof” or words of like import referring to the Credit Agreement shall mean and be a reference to the Modified Credit Agreement.

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Consent to the Fifth Amended and Restated Credit Agreement

(b) The Credit Agreement as specifically modified by this Consent is and shall continue to be in full force and effect and is hereby in all respects ratified and confirmed. This Consent shall be a “Loan Document” for purposes of the definition thereof in the Modified Credit Agreement.

(c) Except as expressly set forth herein, the execution, delivery and effectiveness of this Consent shall not operate as a waiver of any right, power or remedy of any Lender or the Administrative Agent under any of the Loan Documents, nor constitute a waiver of any other provision of any of the Loan Documents.

Section 7. Release of Claims. Each Loan Party, on behalf of itself and its successors and assigns, and its present and former shareholders, affiliates, subsidiaries, divisions, predecessors, directors, officers, attorneys, employees, agents and other representatives (each Loan Party and all such other Persons being hereinafter referred to collectively as the “Releasing Parties” and individually as a “Releasing Party”), hereby absolutely, unconditionally and irrevocably releases, remises and forever discharges the Administrative Agent and the Lenders, and their successors and assigns, and their present and former shareholders, affiliates, subsidiaries, divisions, predecessors, directors, officers, attorneys, employees, agents and other representatives (the Administrative Agent, the Lenders and all such other Persons being hereinafter referred to collectively as the “Releasees” and individually as a “Releasee”), of and from all demands, actions, causes of action, suits, covenants, contracts, controversies, agreements, promises, sums of money, accounts, bills, reckonings, damages and any and all other claims, counterclaims, defenses, rights of set-off, demands and liabilities whatsoever (individually, a “Claim” and collectively, “Claims”) of every kind and nature, known or unknown, suspected or unsuspected, at law or in equity (other than Claims to the extent resulting from the gross negligence or willful misconduct on the part of, or breach of the terms of this Consent (but not of any other Loan Document) by, any Releasee, as determined in a final non-appealable judgment by a court of competent jurisdiction), which Borrower, each Loan Party, any Releasing Party or any of their successors, assigns, or other legal representatives may now or hereafter own, hold, have or claim to have against the Releasees or any of them for, upon, or by reason of any circumstance, action, cause or thing whatsoever which arises at any time on or prior to the Consent Effective Date for or on account of, or in relation to, or in any way in connection with the Credit Agreement or the other Loan Documents or the transactions hereunder or thereunder.

Each Borrower and each Loan Party understands, acknowledges and agrees for itself and on behalf of the other Releasing Parties that the release set forth above may be pleaded as a full and complete defense and may be used as a basis for an injunction against any action, suit or other proceeding which may be instituted, prosecuted or attempted in breach of the provisions of such release.

Each Borrower and each Loan Party agrees for itself and on behalf of the other Releasing Parties that no fact, event, circumstance, evidence or transaction which could now be asserted or which may hereafter be discovered shall affect in any manner the final, absolute and unconditional nature of the release set forth above.

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Consent to the Fifth Amended and Restated Credit Agreement

SECTION 1542 WAIVER. To the extent that the foregoing releases are releases to which Section 1542 of the California Civil Code or similar provisions of other applicable law applies, it is the intention of the parties hereto that the foregoing releases shall be effective as a bar to any and all Claims of whatsoever character, nature and kind, known or unknown, suspected or unsuspected specified herein. In furtherance of this intention, the Releasing Parties expressly waive any and all rights and benefits conferred upon them by the provisions of Section 1542 of the California Civil Code or similar provisions of applicable law, which are as follows:

A GENERAL RELEASE DOES NOT EXTEND TO CLAIMS WHICH THE CREDITOR DOES NOT KNOW OR SUSPECT TO EXIST IN HIS OR HER FAVOR AT THE TIME OF EXECUTING THE RELEASE, WHICH IF KNOWN BY HIM OR HER MUST HAVE MATERIALLY AFFECTED HIS OR HER SETTLEMENT WITH THE DEBTOR.

The parties hereto acknowledge that the foregoing waiver of the provisions of Section 1542 of the California Civil Code was bargained for separately. Thus, notwithstanding the provisions of Section 1542, and for the purpose of implementing a full and complete release and discharge of the Releasees, each party hereto expressly acknowledges that this Consent is intended to include in its effect without limitation all of the claims, causes of action and liabilities of the Releasing Parties which each of them do not know or suspect to exist in their favor at the time of execution of this Consent, and this Consent contemplates extinguishment of all such claims, causes of action and liabilities.

Section 8. Reaffirmation. Each Loan Party hereby (a) acknowledges the existence, validity and enforceability of this Consent and the Additional Amount Payment Letter, (b) confirms and ratifies all of its obligations under the Modified Credit Agreement, the Guaranty, each Security Document and each other Loan Document to which it is party (including, without limitation, its respective guarantees, pledges, grants of security interests and other obligations, as applicable, under and subject to the terms of any such Security Document and other Loan Document to which it is party), and (c) agrees that such guarantees, pledges, grants of security interests and other obligations, and the terms of any Security Document and each of the other Loan Documents to which it is party, are not impaired or adversely affected in any manner whatsoever and shall continue to be in full force and effect in accordance with their terms and, as applicable, shall guarantee and secure all Obligations under the Modified Credit Agreement. The parties hereto acknowledge and agree that all references to the “Credit Agreement” (or words of similar import) in any Loan Document refer to the Modified Credit Agreement without impairing any such obligations or Liens in any respect.

Section 9. Execution in Counterparts. This Consent may be executed in counterparts (and by different parties hereto on different counterparts), each of which shall constitute an original, but all of which when taken together shall constitute a single contract. Delivery of an executed counterpart of a signature page of this Consent by telecopy or other electronic transmission shall be effective as delivery of a manually executed counterpart of this Consent.

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Consent to the Fifth Amended and Restated Credit Agreement

Section 10. GOVERNING LAW; CONSENT TO JURISDICTION.

(a) THIS CONSENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HEREUNDER SHALL BE GOVERNED BY, AND SHALL BE CONSTRUED AND ENFORCED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK, WITHOUT GIVING EFFECT TO THE CONFLICTS OF LAWS PRINCIPLES THEREOF, BUT INCLUDING SECTION 5-1401 OF THE NEW YORK GENERAL OBLIGATIONS LAW.

(b) EACH PARTY HERETO IRREVOCABLY AND UNCONDITIONALLY SUBMITS, FOR THEMSELVES AND THEIR PROPERTY, TO THE EXCLUSIVE JURISDICTION OF THE COURTS OF THE STATE OF NEW YORK SITTING IN NEW YORK CITY IN THE BOROUGH OF MANHATTAN OR, TO THE EXTENT PERMITTED BY LAW, OF THE UNITED STATES DISTRICT COURT OF THE SOUTHERN DISTRICT OF NEW YORK, AND ANY APPELLATE COURT FROM ANY THEREOF, IN ANY ACTION OR PROCEEDING ARISING OUT OF OR RELATING TO THIS CONSENT OR ANY OTHER LOAN DOCUMENT, OR FOR RECOGNITION OR ENFORCEMENT OF ANY JUDGMENT, AND EACH OF THE PARTIES HERETO IRREVOCABLY AND UNCONDITIONALLY AGREES THAT ALL CLAIMS IN RESPECT OF ANY SUCH ACTION OR PROCEEDING MAY BE HEARD AND DETERMINED IN SUCH COURTS. EACH OF THE PARTIES HERETO AGREES THAT A FINAL JUDGMENT IN ANY SUCH ACTION OR PROCEEDING SHALL BE CONCLUSIVE AND MAY BE ENFORCED IN OTHER JURISDICTIONS BY SUIT ON THE JUDGMENT OR IN ANY OTHER MANNER PROVIDED BY LAW. NOTHING IN THIS CONSENT OR IN ANY OTHER LOAN DOCUMENT SHALL AFFECT ANY RIGHT THAT ADMINISTRATIVE AGENT OR ANY LENDER MAY OTHERWISE HAVE TO BRING ANY ACTION OR PROCEEDING RELATING TO THIS CONSENT OR ANY OTHER LOAN DOCUMENT AGAINST BORROWERS OR ANY OTHER LOAN PARTY OR ITS PROPERTIES IN THE COURTS OF ANY JURISDICTION.

(c) EACH BORROWER AND EACH OTHER LOAN PARTY IRREVOCABLY AND UNCONDITIONALLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY OBJECTION THAT IT MAY NOW OR HEREAFTER HAVE TO THE LAYING OF VENUE OF ANY ACTION OR PROCEEDING ARISING OUT OF OR RELATING TO THIS CONSENT OR ANY OTHER LOAN DOCUMENT IN ANY COURT REFERRED TO IN PARAGRAPH (B) OF THIS SECTION. EACH OF THE PARTIES HERETO HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, THE DEFENSE OF AN INCONVENIENT FORUM TO THE MAINTENANCE OF SUCH ACTION OR PROCEEDING IN ANY SUCH COURT.

(d) EACH PARTY HERETO IRREVOCABLY CONSENTS TO SERVICE OF PROCESS IN THE MANNER PROVIDED FOR NOTICES IN SECTION 10.3 OF THE CREDIT AGREEMENT. NOTHING IN THIS CONSENT WILL AFFECT THE RIGHT OF ANY PARTY HERETO TO SERVE PROCESS IN ANY OTHER MANNER PERMITTED BY APPLICABLE LAW.

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Consent to the Fifth Amended and Restated Credit Agreement

Section 11. WAIVER OF JURY TRIAL. EACH PARTY HERETO HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY RIGHT IT MAY HAVE TO A TRIAL BY JURY IN ANY LEGAL PROCEEDING DIRECTLY OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS CONSENT OR ANY OTHER LOAN DOCUMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY OR THEREBY (WHETHER BASED ON CONTRACT, TORT OR ANY OTHER THEORY)

Section 12. Headings. The headings of the sections and subsections hereof are provided for convenience only and shall not in any way affect the meaning or construction of any provision of this Consent.

Section 13. Severability. Any provision of this Consent held to be invalid, illegal or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such invalidity, illegality or unenforceability without affecting the validity, legality and enforceability of the remaining provisions hereof; and the invalidity of a particular provision in a particular jurisdiction shall not invalidate such provision in any other jurisdiction.

Section 14. Administrative Agent. By executing this Consent, the Majority Lenders hereby direct the Administrative Agent to execute this Consent.

[Signature Pages Follow]

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Consent to the Fifth Amended and Restated Credit Agreement

IN WITNESS WHEREOF, the parties hereto have caused this Consent to be duly executed and delivered by their respective proper and duly authorized officers as of the day and year first above written.

Signature Page to Consent to the Fifth Amended and Restated Credit Agreement

Signature Page to Consent to the Fifth Amended and Restated Credit Agreement

Signature Page to Consent to the Fifth Amended and Restated Credit Agreement

Signature Page to Consent to the Fifth Amended and Restated Credit Agreement