Exhibit 99.1

FORM OF INSTRUCTIONS

AS TO USE OF

STEREOTAXIS, INC.

RIGHTS CERTIFICATES

CONSULT THE RIGHTS AGENT, YOUR BANK OR BROKER

AS TO ANY QUESTIONS

The following instructions relate to a rights offering (the “Rights Offering”) by Stereotaxis, Inc., a Delaware corporation (“Stereotaxis”), to the holders of record (the “Recordholders”) of its common stock, par value $0.001 per share (the “Common Stock”), as described in the accompanying Stereotaxis prospectus dated , 2013 (the “Prospectus”). Recordholders as of 5:00 p.m. New York City time on , 2013 (the “Record Date”) are receiving, at no charge, transferable subscription rights (the “Rights”) to subscribe for and purchase shares of Common Stock (the “Underlying Shares”). In the Rights Offering, Stereotaxis is offering an aggregate of up to 6,315,953 Underlying Shares.

Each Recordholder will receive a Right to purchase one-third of a share of common stock at a price of $3.00 per share (the “Subscription Price”) for each whole share of our common stock owned by such Recordholder as of 5:00 p.m., New York City time, on the Record Date. The Rights will expire if not exercised prior to 5:00 p.m., New York City time, on , 2013, unless extended (the “Expiration Time”). Only whole rights are exercisable. Fractional rights remaining after aggregating all of the rights distributed to you will be rounded down to the nearest whole number. You will not receive any payment with respect to fractional rights that are rounded down. Any excess subscription payments received by the Rights Agent will be returned, without interest, as soon as practicable. For example, if a holder of Rights owned 200 shares of Common Stock as of 5:00 p.m., New York City time on the Record Date, it would receive the right to purchase 66 shares of Common Stock for the Subscription Price.

Each Rights holder will be required to submit payment in full for all the shares it wishes to buy with its Rights.

Fractional Rights remaining after aggregating all of the Rights distributed to you will be rounded down to the nearest whole number.

Stereotaxis will not be required to issue shares of Common Stock to you if the Rights Agent does not receive your payment (whether delivered directly in case you are a Recordholder or indirectly through a Recordholder in the case you are a beneficial owner but not a Recordholder) prior to the Expiration Time, regardless of when you send the subscription payment and related documents, unless you send the documents in compliance with the guaranteed delivery procedures described below. The period for exercising your Rights may be extended by Sterotaxis in its sole discretion. If the expiration date of the rights offering is so extended, Stereotaxis will give oral or written notice to the Rights Agent on or before the scheduled expiration date and Stereotaxis will issue a press release announcing such extension no later than 9:00 a.m., New York City time, on the next business day after the most recently announced expiration of the rights offering. Stereotaxis will extend the duration of the Rights Offering as required by applicable law or regulation and may choose to extend it. Stereotaxis does not

currently intend to extend the expiration of the Rights offering. To the extent that any completed subscription exercise documentation is received by the Rights Agent after the expiration of the Rights Offering, Stereotaxis may, in its sole discretion, choose to accept such subscription, but it shall be under no obligation to do so. The Rights will be evidenced by transferable Rights certificates (the “Rights Certificates”).

The number of Rights to which you are entitled is printed on the face of your Rights Certificate. You should indicate your wishes with regard to the exercise of your Rights by completing the appropriate portions of your Rights Certificate and returning the certificate to the Rights Agent in the envelope provided.

YOUR RIGHTS CERTIFICATES, OR NOTICE OF GUARANTEED DELIVERY, AND SUBSCRIPTION PRICE PAYMENT FOR EACH RIGHTS THAT IS EXERCISED PURSUANT TO THE RIGHTS, INCLUDING FINAL CLEARANCE OF ANY CHECKS, MUST BE RECEIVED BY THE RIGHTS AGENT, ON OR BEFORE THE EXPIRATION TIME. ONCE A RIGHTS HOLDER HAS EXERCISED THE RIGHTS, SUCH EXERCISE MAY NOT BE REVOKED. RIGHTS NOT EXERCISED PRIOR TO THE EXPIRATION TIME OF THE RIGHTS OFFERING WILL EXPIRE.

1. Method of Subscription—Exercise of Rights.

To exercise Rights, complete your Rights Certificate and send the properly completed and executed Rights Certificate evidencing such Rights with any signatures required to be guaranteed so guaranteed, together with payment in full of the Subscription Price for each Underlying Share subscribed for pursuant to the Rights, to the Rights Agent, on or prior to the Expiration Time. Payment of the aggregate Subscription Price will be held in a segregated account to be maintained by the Rights Agent. All payments must be made in U.S. dollars for the full number of Underlying Shares being subscribed for (a) check or bank draft payable to Broadridge Corporate Issuer Solutions, Inc. upon a U.S. bank, (b) postal, telegraphic or express money order payable to the Rights Agent, or (c) wire transfer of immediately available funds to accounts maintained by the Rights Agent for purposes of accepting subscriptions in the Rights Offering at [        ] (the “Subscription Account”). Any wire transfer should clearly indicate the identity of the subscriber who is paying the Subscription Price by wire transfer. Payments will be deemed to have been received upon (i) clearance of any uncertified check, (ii) receipt by the Rights Agent of any certified check or bank draft drawn upon a U.S. bank or of any postal, telegraphic or express money order or (iii) receipt of collected funds in the Subscription Account designated above. If paying by uncertified personal check, please note that the funds paid thereby may take five or more business days to clear. Accordingly, Rights holders who wish to pay the aggregate Subscription Price by means of uncertified personal check are urged to make payment sufficiently in advance of the Expiration Time to ensure that such payment is received and clears by such date and are urged to consider payment by means of certified or cashier’s check, money order or wire transfer of funds.

The Rights Certificate and payment of the aggregate Subscription Price if by check or bank draft drawn upon a U.S. bank or postal, telegraphic or express money order, or, if applicable, Notices of Guaranteed Delivery (as defined below) must be delivered to the Rights Agent by hand delivery, first class mail or courier service to:

By hand or overnight courier:

Broadridge Corporate Issuer Solutions, Inc.

Attn: Re-Organization Dept.,

1981 Marcus Ave., Suite 100

Lake Success, NY 11042-1046.

By mail:*

Broadridge Corporate Issuer Solutions, Inc.

Attn: Re-Organization Dept., P.O. Box 1317

Brentwood, NY 11717.

Delivery to an address other than the applicable address above does not constitute valid delivery.

If you have any questions, require assistance regarding the method of exercising Rights or require additional copies of relevant documents, please contact the Rights Agent, Broadridge Corporate Issuer Solutions, Inc. at (855) 300-4994.

By making arrangements with your bank or broker for the delivery of funds on your behalf, you may also request such bank or broker to exercise the Rights Certificate on your behalf. Alternatively, you may cause a written guarantee, a copy of which is being furnished to you (the “Notice of Guaranteed Delivery”), from a member firm of a registered national securities exchange or a member of the Financial Industry Regulatory Authority, or from a commercial bank or trust company having an office or correspondent in the United States or from a bank, shareholder, savings and loan association or credit union with membership in an approved signature guarantee medallion program, pursuant to Rule 17Ad-15 of the Securities Exchange Act of 1934, as amended, (each, an “Eligible Institution”), to be received by the Rights Agent on or prior to the Expiration Time together with payment in full of the applicable Subscription Price. Such Notice of Guaranteed Delivery must state your name, the number of Rights represented by the Rights Certificate or Rights Certificates held by you, the number of Underlying Shares being subscribed for pursuant to the Rights and that you will guarantee the delivery to the Rights Agent of any properly completed and executed Rights Certificate or Rights Certificates evidencing such Rights within three (3) business days following the date of the Notice of Guaranteed Delivery. If this procedure is followed, the properly completed Rights Certificate or Rights Certificates evidencing the Right or Rights being exercised, with any signatures required to be guaranteed so guaranteed, must be received by the Rights Agent within three (3) business days following the date of the Notice of Guaranteed Delivery. The Notice of Guaranteed Delivery may be delivered to the Rights Agent in the same manner as Rights Certificates at the address set forth above. Additional copies of the Notice of Guaranteed Delivery may be obtained upon request from the Rights Agent at the address set forth above, or by calling the Rights Agent at (855) 300-4994.

If you do not indicate the number of Rights being exercised, or do not forward full payment of the Subscription Price, then you will be deemed to have exercised your Rights with respect to the maximum number of whole Rights that may be exercised with the aggregate Subscription Price you delivered to the Rights Agent. If Stereotaxis does not apply your full Subscription Price payment to your purchase of shares of Common Stock, the excess subscription payment received by the Rights Agent will be returned to you, without interest, as soon as practicable.

2. Issuance of Common Stock.

The following deliveries and payments will be made to the address shown on the face of your Rights Certificate, unless you provide instructions to the contrary in your Rights Certificate.

(a) Rights. As soon as practicable after the closing of the Rights Offering and the valid exercise of Rights, the Rights Agent will mail to each Rights holder that validly exercises the Right certificates representing shares of Common Stock purchased pursuant to the Rights.

(b) Excess Cash Payments. As soon as practicable after the Expiration Time, any excess subscription payments received in payment of the Subscription Price by the Rights Agent will be mailed to each Rights holder, without interest.

3. Sale or Transfer of Rights.

The Rights granted to you will be transferable during the course of the Rights Offering, and the Rights are listed on the Nasdaq Capital Market under the symbol “STXS”. As a result, you may transfer or sell your Rights if you do not want to purchase any shares of our Common Stock. If you purchase Rights in the open market or otherwise, and the Rights Offering is not completed, the purchase price paid for such Rights will not be returned to you.

4. Execution.

(a) Execution by Registered Holder. The signature on the Rights Certificate must correspond with the name of the registered holder exactly as it appears on the face of the Rights Certificate without any alteration or change whatsoever. Persons who sign the Rights Certificate in a representative or other fiduciary capacity must indicate their capacity when signing and, unless waived by the Rights Agent in its sole and absolute discretion, must present to the Rights Agent satisfactory evidence of their authority to so act.

(b) Execution by Person Other than Registered Holder. If the Rights Certificate is executed by a person other than the holder named on the face of the Rights Certificate, proper evidence of authority of the person executing the Rights Certificate must accompany the same unless, for good cause, the Rights Agent dispenses with proof of authority.

(c) Signature Guarantees. Your signature must be guaranteed by an Eligible Institution (as defined above) if you specify special delivery instructions. See the “Form of Election to Purchase” attached to your Rights Certificate(s).

5. Method of Delivery.

The method of delivery of Rights Certificates and payment of the aggregate Subscription Price to the Rights Agent will be at the election and risk of the Rights holder. However, if you elect to exercise your Rights, Stereotaxis urges you to consider using a certified or cashier’s check, money order, or wire transfer of funds to ensure that the Rights Agent receives your funds prior to the Expiration Time. If you send an uncertificated check, payment will not be deemed to have been received by the Rights Agent until the check has cleared, but if you send a certified check, bank draft drawn upon a U.S. bank, a postal, telegraphic or express money order or wire or transfer funds directly to the Rights Agent’s account, payment will be deemed to have been received by the Rights Agent immediately upon receipt of such instruments and wire or transfer. Any personal check used to pay for shares of Common Stock must clear the appropriate financial institutions prior to the Expiration Time. The clearinghouse may require five or more business days. Accordingly, Rights holders that wish to pay the aggregate Subscription Price by means of an uncertified personal check are urged to make payment sufficiently in advance of the Expiration Time to ensure such payment is received and clears by such date.

6. Special Provisions Relating to the Delivery of Rights through the Depository Trust Company.

In the case of Rights that are held of record through The Depository Trust Company (“DTC”), exercises of the Rights may be effected by instructing DTC to transfer Rights from the DTC account of such holder to the DTC account of the Rights Agent, together with certification as to the aggregate number of Rights exercised subscribed for pursuant to the Rights by each beneficial owner of Rights on whose behalf such nominee is acting, and payment to the Rights Agent of the Subscription Price for each share of Common Stock subscribed for pursuant to the Rights. See the Company’s “Letter to Shareholders” and “Form of Election to Purchase” attached to your Rights Certificate(s).

7. Substitute Form W-9.

TO ENSURE COMPLIANCE WITH IRS CIRCULAR 230, YOU ARE HEREBY NOTIFIED THAT: (A) ANY DISCUSSION OF U.S. FEDERAL TAX ISSUES CONTAINED OR REFERRED TO HEREIN IS NOT INTENDED OR WRITTEN TO BE USED, AND CANNOT BE USED BY ANY TAXPAYER FOR THE PURPOSE OF AVOIDING U.S. FEDERAL, STATE OR LOCAL TAX PENALTIES, (B) SUCH DISCUSSION IS WRITTEN IN CONNECTION WITH THE PROMOTION OR MARKETING OF THE TRANSACTION OR MATTERS DISCUSSED HEREIN, AND (C) THE TAXPAYER SHOULD SEEK ADVICE BASED ON THEIR PARTICULAR CIRCUMSTANCES FROM AN INDEPENDENT TAX ADVISOR.

Each Rights holder who elects to exercise Rights should provide the Rights Agent with a correct Taxpayer Identification Number (“TIN”) on Substitute Form W-9, a copy of which is being furnished to each Rights holder. Additional copies of Substitute Form W-9 may be obtained upon request from the Rights Agent at the address set forth above or by calling the Rights Agent at (855) 300-4994. Failure to provide the information on the form may subject such holder to a $50.00 penalty for each such failure and to U.S. federal income tax backup withholding (currently at a 28% rate) with respect to dividends that may be paid by Stereotaxis on shares of Common Stock purchased upon the exercise of Rights (for those holders exercising Rights).

8. Determinations Regarding the Exercise of Your Rights.

Stereotaxis will decide, in its sole discretion, all questions concerning the timeliness, validity, form, and eligibility of the exercise of your Rights. Any such determinations by Stereotaxis will be final and binding. Stereotaxis, in its sole discretion, may waive, in any particular instance, any defect or irregularity or permit, in any particular instance, a defect or irregularity to be corrected within such time as Stereotaxis may determine. Stereotaxis will not be required to make uniform determinations in all cases. Stereotaxis may reject the exercise of any of your Rights because of any defect or irregularity. Stereotaxis will not accept any exercise of Rights until all irregularities have been waived by Stereotaxis or cured by you within such time as Stereotaxis decides, in its sole discretion.

Neither Stereotaxis nor the Rights Agent will be under any duty to notify you of any defect or irregularity in connection with your submission of Rights Certificates, and Stereotaxis will not be liable for failure to notify you of any defect or irregularity. Stereotaxis reserves the right to reject your exercise of Rights if Stereotaxis determines that your exercise is not in accordance with the terms of the rights offering, as set forth in the Prospectus and these Instructions for Use, or in proper form. Stereotaxis will also not accept the exercise of your Rights if Stereotaxis’s issuance of shares of Common Stock to you could be deemed unlawful under applicable law.