Exhibit 10.1

FORM OF AMENDMENT AND EXCHANGE AGREEMENT

This Amendment and Exchange Agreement (the “Agreement”), dated as of August 7, 2013, is by and between Stereotaxis, Inc., a Delaware corporation with offices located at 4320 Forest Park Avenue, Suite 100, St. Louis, MO 63108 (the “Company”), and the holder identified on the signature page hereto (“Holder”).

R E C I T A L S

A. Prior to the date hereof, the Company has issued to the Holder (i) a subordinated convertible debenture (the “Debenture”), which Debenture is convertible into shares of the Company’s common stock, $0.001 par value per share (the “Common Stock”) (as converted, collectively, the “Conversion Shares”), in accordance with the terms of the Debenture and (ii) a warrant (the “Warrant”) to purchase Common Stock (the “Warrant Shares”), in each case, pursuant to a Securities Purchase Agreement, dated as of May 7, 2013 (the “Securities Purchase Agreement”) to the Holder and certain other investors signatory thereto (the Holder and such other investors collectively, the “Investors”). Capitalized terms not defined herein shall have the meanings set forth in the Securities Purchase Agreement as amended hereby.

B. On or prior to the date hereof, (i) except for such aggregate portion of the principal amount of the Debenture as described below the Holder’s name on the signature page of the Holder (the “Remaining Debenture”), the Holder has converted (or delivered conversion notice(s) electing to convert) the Debenture in full pursuant to the terms of the Debenture and (ii) the Holder has exercised (or delivered irrevocable exercise notice(s) electing to exercise) the Warrant in full pursuant to the terms of the Warrant.

C. The Company and the Holder desire to enter into this Agreement, pursuant to which, among other things (i) the Company and the Holder shall exchange the Remaining Debenture for (x) such number of shares of Common Stock as described below the Holder’s name on the signature page of the Holder (the “Exchange Shares”) and (y) a new warrant to purchase such number of shares of Common Stock as described below the Holder’s name on the signature page of the Holder, in the form attached hereto as Exhibit A (the “Exchange Warrant”, and such shares of Common Stock issuable upon exercise thereof, the “Exchange Warrant Shares”), and (ii) certain covenants of the subordinated convertible debentures of the Company (including the Debenture, the “Debentures”) and the Securities Purchase Agreement shall be removed.

D. Concurrently with the transactions contemplated hereby, Investors (other than the Holder) (the “Other Holders”), which, together with the Holder, beneficially own at least 75% of the aggregate principal amount of subordinated convertible debentures of the Company (the “Required Holders”), are executing agreements identical to this Agreement (other than proportional changes in the numbers reflecting the different aggregate principal amount of subordinated convertible debentures and related warrants of the Company held by each Other Holder and corresponding proportional changes to the number of shares of Common Stock and new warrants to purchase Common Stock to be delivered to such Other Holder in exchange for such portion of the applicable subordinated convertible debenture being exchanged) (the “Other Agreements”, and together with this Agreement, the “Agreements”).

E. The Remaining Debenture will be exchanged for the Exchange Shares and the Exchange Warrant in an exchange made in reliance upon the exemption from registration provided by Section 3(a)(9) of the Securities Act.

A G R E E M E N T

1. Amendment; Exchange. On the Closing Date (as defined below), the Holder shall, and the Company shall, pursuant to Section 3(a)(9) of the Securities Act, exchange (a) the Remaining Debenture for the Exchange Shares and the Exchange Warrant (collectively, the “Exchange”). On or prior to the Closing (as defined below), the following transactions shall occur:

1.1 Delivery. On the Closing Date, the Company shall deliver the Exchange Shares and the Exchange Warrant to the Holder and (b) the Remaining Debenture shall be extinguished. The Holder acknowledges that, as of the Effective Time, the Holder has no knowledge of any outstanding defaults under the Debenture. The Exchange Shares and the Exchange Warrant shall be issued without any restricted legend and shall be delivered to the Holder (or, with respect to the Exchange Shares, by Deposit/Withdrawal at Custodian to the broker of the Holder) in accordance with the instructions set forth on the signature page of the Holder.

1.2 Other Documents. The Company and the Holder shall execute and/or deliver such other documents and agreements as are customary and reasonably necessary to effectuate the Amendment and the Exchange.

1.3 No Additional Consideration. The parties acknowledge and agree that the Exchange Shares and the Exchange Warrant shall be issued to the Holder in exchange for the Remaining Debenture without the payment of any additional consideration.

1.4 Closing. Upon confirmation that the Required Holders shall have executed the Amendment and Exchange Agreements, the closing of the Exchange (the “Closing”) shall occur on August 7, 2013 or such other date as is mutually acceptable to the Holder and the Company (the “Closing Date”).

2. AMENDMENTS TO TRANSACTION DOCUMENTS.

2.1 Amendments to Transaction Documents; Waivers.

(a) Effective as of the Effective Time, each of the Transaction Documents are hereby amended as follows:

(i) The defined term “Conversion Shares” is hereby amended to include “each of the “Exchange Shares” (as defined in the Amendment and Exchange Agreements)”.

(ii) The defined term “Warrants” is hereby amended to include “each “Exchange Warrant” (as defined in the Amendment and Exchange Agreements)”.

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(iii) The defined term “Transaction Documents” is hereby amended to include the Amendment and Exchange Agreements.

(iv) The defined term “Amendment and Exchange Agreements” shall mean “those certain Amendment and Exchange Agreements, dated as of August     , 2013, each by and between the Company and each Buyer”.

(v) Each of Sections 4(d), 4(j), 4(k), 4(n), 4(r), 4(t), 4(u) and 4(v) of the Securities Purchase Agreement are hereby amended and restated as “[Intentionally Omitted]”. The second sentence of Section 4(f) is hereby amended and restated as follows:

So long as any Warrants remain outstanding, the Company shall maintain the Common Stock’s listing or designation for quotation (as the case may be) on the Principal Market, the New York Stock Exchange, the NYSE Amex, the Nasdaq Capital Market or the Nasdaq Global Select Market (each, an “Eligible Market”).

(vi) Section 14 of each of the Debentures are hereby amended and restated as “[Intentionally Omitted]”.

3. REPRESENTATIONS AND WARRANTIES.

3.1 Holder Bring Down. The Holder hereby makes the representations and warranties as to itself only as set forth in Section 2 of the Securities Purchase Agreement (as amended hereby) as if such representations and warranties were made as of the date hereof and set forth in their entirety in this Agreement, mutatis mutandis.

3.2 Company Bring Down. Subject to such disclosures set forth in the Company’s filings with the Securities and Exchange Commission prior to the date hereof and in the 8-K Filing (as defined below), the Company hereby makes the representations and warranties to the Holder as set forth in Section 3 of the Securities Purchase Agreement (as amended hereby) as if such representations and warranties were made as of the date hereof and set forth in their entirety in this Amendment, mutatis mutandis.

4. Covenants.

4.1 Disclosure of Transactions and Other Material Information. On or before 9:30 a.m., New York time, on the first (1st) Business Day following the date of this Agreement, the Company shall file a Current Report on Form 8-K describing all the material terms of the transactions contemplated by the Agreements in the form required by the 1934 Act and attaching all the material agreements (including, without limitation, this Agreement and the form of the Exchanged Warrants) (including all attachments, the “8-K Filing”). From and after the issuance of the 8-K Filing, the Company shall have disclosed all material, non-public information (if any) delivered to any of the Buyers by the Company or any of its Subsidiaries, or any of their respective officers, directors, employees or agents in connection with the transactions contemplated by the Agreements.

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4.2 Fees. The Company shall reimburse Greenberg Traurig, LLP (counsel to the lead Investor), on demand, for all reasonable, documented costs and expenses incurred by it in connection with preparing and delivering this Agreement (including, without limitation, all reasonable, documented legal fees and disbursements in connection therewith, and due diligence in connection with the transactions contemplated thereby), which amount shall not exceed $15,000 without the consent of the Company (the “Lead Investor Counsel Expenses”).

4.3 Holding Period. For the purposes of Rule 144, the Company acknowledges that the holding period of (i) the Remaining Debenture may be tacked onto the holding period of each of the Exchange Shares and the Exchange Warrant, and the Company agrees not to take a position contrary to this Section 4.3. The Company agrees to take all actions, including, without limitation, obtaining customary legal opinions necessary to comply with the foregoing.

4.4 Release. The Holder hereby releases the Company from any and all claims, demands, debts and causes of action, known or unknown, past, present or future, arising from any defaults, if any, previously disclosed to the Holder and outstanding as of the date hereof under the Debenture, the Warrant and/or any other Transaction Documents; provided, that notwithstanding anything contained herein to the contrary, this release shall not release the Company from any of its obligations under this Agreement or any other Exchange Document or related to any outstanding conversion notice pursuant to the Debenture or exercise notice pursuant to the Warrant.

5. MISCELLANEOUS.

5.1 Effective Time. This amendments set forth in Section 2 of this Agreement shall be effective upon the later of (x) the time the Company shall have paid Lead Investor Counsel Expenses to Greenberg Traurig LLP by wire transfer of U.S. dollars and immediately available funds in accordance with the written instructions of Greenberg Traurig LLP delivered to the Company and (y) the date each of the Required Holders shall have received such shares of Common Stock and warrants to Purchase Common Stock in exchange for the Debentures subject to exchange as contemplated by each of their respective Amendment and Exchange Agreements (the “Effective Time”).

5.2 Miscellaneous Provisions. Section 9 of the Securities Purchase Agreement (as amended hereby) is hereby incorporated by reference herein, mutatis mutandis.

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5.3 Most Favored Nation. The Company hereby represents and warrants as of the date hereof and covenants and agrees from and after the date hereof that none of the terms offered to any Person with respect to any consent, release, amendment, settlement or waiver relating to the terms, conditions and transactions contemplated hereby (each a “Settlement Document”), is or will be more favorable to such Person than those of the Holder and this Agreement. If, and whenever on or after the date hereof, the Company enters into a Settlement Document, then (i) the Company shall provide notice thereof to the Holder immediately following the occurrence thereof and (ii) the terms and conditions of this Agreement, the other Exchange Documents and the Securities (other than any limitations on conversion or exercise set forth therein) shall be, without any further action by the Holder or the Company, automatically amended and modified in an economically and legally equivalent manner such that the Holder shall receive the benefit of the more favorable terms and/or conditions (as the case may be) set forth in such Settlement Document, provided that upon written notice to the Company at any time the Holder may elect not to accept the benefit of any such amended or modified term or condition, in which event the term or condition contained in this Agreement or the Securities (as the case may be) shall apply to the Holder as it was in effect immediately prior to such amendment or modification as if such amendment or modification never occurred with respect to the Holder. The provisions of this Section 5.3 shall apply similarly and equally to each Settlement Document.

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the day and year first above written.

[Amendment and Exchange Agreement]

IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the day and year first above written.

[Amendment and Exchange Agreement]