Exhibit 10.1

EXECUTION VERSION

FIRST AMENDMENT TO

FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

This First Amendment to Fourth Amended and Restated Credit Agreement (this “First Amendment”) is entered into as of the 15th day of April, 2011 (the “Effective Date”), by and among GEOMET, INC., a Delaware corporation (“Borrower”), BANK OF AMERICA, N.A., as Administrative Agent (“Administrative Agent”), and the Banks party hereto.

W I T N E S S E T H:

WHEREAS, Borrower, Administrative Agent, the financial institutions party thereto as Banks, and the other agents party thereto are parties to that certain Fourth Amended and Restated Credit Agreement dated as of June 3, 2010 (as amended by that certain letter agreement dated July 15, 2010, the “Credit Agreement”) (unless otherwise defined herein, all terms used herein with their initial letter capitalized shall have the meaning given such terms in the Credit Agreement); and

WHEREAS, pursuant to the Credit Agreement, Banks have made a revolving credit loan to Borrower and provided certain other credit accommodations to Borrower; and

WHEREAS, Borrower has requested that the Banks (a) amend the financial covenants set forth in Article X of the Credit Agreement, including, without limitation, amendment of the Interest Coverage Ratio and the definitions applicable to the calculation of the current ratio, and deletion of the Interest/Cap Ex Coverage Ratio, and (b) reaffirm the Borrowing Base; and

WHEREAS, the Administrative Agent and the Banks are willing to amend the Credit Agreement as set forth herein on the terms and conditions set forth herein.

NOW THEREFORE, for and in consideration of the mutual covenants and agreements herein contained and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged and confessed, Borrower, Administrative Agent and the Banks party hereto hereby agree as follows:

Section 1. Amendments. In reliance on the representations, warranties, covenants and agreements contained in this First Amendment, and subject to the satisfaction of each condition precedent set forth in Section 3, the Credit Agreement shall be amended effective as of the Effective Date in the manner provided in this Section 1.

1.1 Deleted Definitions. Section 1.1 of the Credit Agreement is hereby amended to delete therefrom the definitions of “Capital Expenditure” and “Interest/Cap Ex Coverage Ratio”.

1.2 Additional Definitions. Section 1.1 of the Credit Agreement is hereby amended to add thereto in alphabetical order the following definitions which shall read in full as follows:

“First Amendment” means that certain First Amendment to Fourth Amended and Restated Credit Agreement dated as of April 15, 2011 among Borrower, Administrative Agent and the Banks party thereto.

1.3 Amendments to Definitions. The definitions of “Consolidated Current Assets”, “Consolidated Current Liabilities”, and “Loan Papers” contained in Section 1.1 of the Credit Agreement are hereby amended and restated in their entirety as follows:

“Consolidated Current Assets” means, in the case of Borrower at any time, the sum of (a) the current assets of Borrower and its Consolidated Domestic Subsidiaries at such time determined in accordance with GAAP, plus (b) the Availability at such time. For purposes of this definition, any unrealized gains (net of related deferred taxes recorded on the balance sheet as a current liability) on any Hedge Transaction for any period of determination shall be excluded from the determination of current assets of Borrower and its Consolidated Domestic Subsidiaries.

“Consolidated Current Liabilities” means, in the case of Borrower at any time, the current liabilities of Borrower and its Consolidated Domestic Subsidiaries at such time determined in accordance with GAAP, excluding (a) any current liabilities to pay principal on the Notes and (b) current liabilities of up to $1,500,000 in the aggregate to pay accrued and unpaid Distributions in respect of Convertible Preferred Equity. For purposes of this definition, any unrealized losses (net of related deferred taxes recorded on the balance sheet as a current asset) on any Hedge Transaction for any period of determination shall also be excluded from the determination of current liabilities of Borrower and its Consolidated Domestic Subsidiaries.

“Loan Papers” means this Agreement, the First Amendment, the Notes, each Facility Guaranty now or hereafter executed, the Mortgages, each Borrower Pledge Agreement now or hereafter executed, each Subsidiary Pledge Agreement now or hereafter executed, the Certificate of Effectiveness, the Letters of Credit and all other certificates, documents or instruments delivered in connection with this Agreement, as the foregoing may be amended from time to time.

1.4 Deletion of Interest/Cap Ex Coverage Ratio Provision. Clause (b) of Article X of the Credit Agreement is hereby amended and restated in its entirety to read “[Intentionally Deleted.]”.

1.5 Amendment of Interest Coverage Ratio Provision. Clause (c) of Article X of the Credit Agreement is hereby amended and restated in its entirety as follows:

(c) As of the end of any Fiscal Quarter Borrower will not permit its Interest Coverage Ratio to be less than 2.75 to 1.

2

Section 2. Reaffirmation of Borrowing Base. In reliance on the representations, warranties, covenants and agreements contained in this First Amendment, and subject to the satisfaction of the conditions precedent set forth in Section 3, the Borrowing Base is hereby reaffirmed to be $90,000,000 effective as of the Effective Date and shall remain at $90,000,000 until the next Determination Date. For the purposes of Section 4.2 of the Credit Agreement, the redetermination set forth in this Section 2 will constitute the Periodic Determination for the June 30, 2011 Scheduled Determination Date and shall not be construed or deed to be a Special Determination for purposes of Section 4.3 of the Credit Agreement.

Section 3. Conditions Precedent to Amendment. This Amendment shall be effective as of the Effective Date when the following conditions precedent have been satisfied:

3.1 Amendment/Consent. Administrative Agent shall have received counterparts of this Amendment executed on behalf of Borrower, Administrative Agent and the Required Banks, and of the consent attached to this Amendment executed by GeoMet Operating, GeoMet Gathering, and any other Domestic Subsidiary party to a Facility Guaranty.

Section 4. Representations and Warranties of Borrower. To induce the Banks and Administrative Agent to enter into this First Amendment, Borrower hereby represents and warrants to Banks and Administrative Agent as follows:

4.1 Reaffirm Existing Representations and Warranties. Each representation and warranty of Borrower contained in the Credit Agreement and the other Loan Papers is true and correct on the date hereof and will be true and correct after giving effect to the amendments set forth in Section 1 hereof.

4.2 Due Authorization; No Conflict. The execution, delivery and performance by Borrower of this First Amendment are within Borrower’s corporate powers, have been duly authorized by all necessary action, require no action by or in respect of, or filing with, any governmental body, agency or official and do not violate or constitute a default under any provision of applicable law or any Material Agreement binding upon Borrower or any other Credit Party, or result in the creation or imposition of any Lien upon any of the assets of Borrower or any other Credit Party except Permitted Encumbrances.

4.3 Validity and Enforceability. This First Amendment constitutes the valid and binding obligation of Borrower enforceable in accordance with its terms, except as (a) the enforceability thereof may be limited by bankruptcy, insolvency or similar laws affecting creditor’s rights generally, and (b) the availability of equitable remedies may be limited by equitable principles of general application.

4.4 No Default. No Default or Event of Default shall have occurred which is continuing.

3

Section 5. Miscellaneous.

5.1 Reaffirmation of Loan Papers. Any and all of the terms and provisions of the Credit Agreement and the Loan Papers shall, except as amended and modified hereby, remain in full force and effect. The amendments contemplated hereby shall not limit or impair any Liens securing the Obligations, each of which are hereby ratified, affirmed and extended to secure the Obligations as they may be increased pursuant hereto.

5.2 Parties in Interest. All of the terms and provisions of this First Amendment shall bind and inure to the benefit of the parties hereto and their respective successors and assigns.

5.3 Legal Expenses. Borrower hereby agrees to pay on demand all reasonable fees and expenses of counsel to Administrative Agent incurred by Administrative Agent in connection with the preparation, negotiation and execution of this First Amendment and all related documents.

5.4 Counterparts. This First Amendment may be executed in counterparts, and all parties need not execute the same counterpart; however, no party shall be bound by this First Amendment until Borrower and all Banks have executed a counterpart. Facsimiles or other electronic transmissions (e.g., pdf) shall be effective as originals.

5.5 Complete Agreement. THIS FIRST AMENDMENT, THE CREDIT AGREEMENT AND THE OTHER LOAN PAPERS REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN OR AMONG THE PARTIES.

5.6 Headings. The headings, captions and arrangements used in this First Amendment are, unless specified otherwise, for convenience only and shall not be deemed to limit, amplify or modify the terms of this First Amendment, nor affect the meaning thereof.

5.7 Governing Law. This First Amendment shall be governed by, and construed in accordance with, the laws of the State of New York, other than conflict of laws rules thereof.

IN WITNESS WHEREOF, the parties hereto have caused this First Amendment to be duly executed by their respective authorized officers on the date and year first above written.

[Signature Pages to Follow]

4

[Signature Page]

FIRST AMENDMENT TO FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

GEOMET, INC.

[Signature Page]

FIRST AMENDMENT TO FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

GEOMET, INC.

[Signature Page]

FIRST AMENDMENT TO FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

GEOMET, INC.

[Signature Page]

FIRST AMENDMENT TO FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

GEOMET, INC.

[Signature Page]

FIRST AMENDMENT TO FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

GEOMET, INC.

[Signature Page]

FIRST AMENDMENT TO FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

GEOMET, INC.

The undersigned (i) consents and agrees to this First Amendment, and (ii) agrees that the Loan Papers to which it is a party (including, without limitation, the Facility Guaranty dated as of June 3, 2010) shall remain in full force and effect and shall continue to be the legal, valid and binding obligation of the undersigned, enforceable against it in accordance with its terms.

[Consent Page]

FIRST AMENDMENT TO FOURTH AMENDED AND RESTATED CREDIT AGREEMENT

GEOMET, INC.