Exhibit 5.1

November 13, 2013

Board of Directors

Capstead Mortgage Corporation

8401 North Central Expressway

Suite 800

Dallas, TX 75225

Ladies and Gentlemen:

We are acting as Maryland counsel to Capstead Mortgage Corporation, a Maryland corporation (the “Company”), in connection with the proposed public offering of up to 1,000,000 shares of 7.50% Series E Cumulative Redeemable Preferred Stock, $.10 par value per share (the “Preferred Shares”) that are being offered and sold pursuant to the Company’s Registration Statement on Form S-3 (file no. 333-179607) initially filed with the Securities and Exchange Commission on February 21, 2012 (the “Registration Statement”), all of which Preferred Shares are to be sold by the Company pursuant to the Sales Agency Agreement, dated as of November 12, 2013, by and between the Company and Meyers Associates, LP (dba Brinson Patrick a division of Meyers Associates LP) (the “Agreement”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including telecopies). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

For purposes of this opinion letter, we have assumed that (i) at the time of offer, issuance and sale of the Preferred Shares, the Registration Statement will have been declared effective under the Securities Act of 1933, as amended (the “Act”), and no stop order suspending its effectiveness will have been issued and remain in effect; and (ii) the Preferred Shares and any shares of the Company’s Common Stock, par value $.01 per share, issuable upon conversion of the Preferred Shares subject to a maximum amount of 3,813,880 shares (the “Conversion Shares”) will not be issued in violation of the ownership limit contained in the Company’s Articles of Incorporation, as amended and supplemented.

Hogan Lovells US LLP is a limited liability partnership registered in the District of Columbia. “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in: Alicante    Amsterdam    Baltimore    Beijing    Berlin    Brussels    Caracas    Colorado Springs    Denver    Dubai    Dusseldorf    Frankfurt    Hamburg    Hanoi    Ho Chi Minh City    Hong Kong    Houston    London    Los Angeles    Madrid    Miami Milan    Moscow    Munich    New York    Northern Virginia    Paris    Philadelphia    Prague    Rio de Janeiro    Rome    San Francisco    Shanghai   Silicon Valley Singapore    Tokyo    Ulaanbaatar    Warsaw    Washington DC    Associated offices: Budapest    Jakarta    Jeddah    Riyadh    Zagreb. For more information see www.hoganlovells.com

This opinion letter is based as to matters of law solely on the applicable provisions of the Maryland General Corporation Law, as amended and currently in effect. We express no opinion herein as to any other laws, statutes, ordinances, rules, or regulations (and in particular, we express no opinion as to any effect that such other laws, statutes, ordinances, rules, or regulations may have on the opinions expressed herein).

Based upon, subject to and limited by the foregoing, we are of the opinion that:

(a) The Preferred Shares, upon issuance pursuant to the Agreement and receipt by the Company of the consideration specified in the resolutions of the Board of Directors of the Company authorizing the Preferred Shares, will be validly issued, fully paid and nonassessable.

(b) The Conversion Shares, upon issuance pursuant to the terms of and in exchange for the Preferred Shares, will be validly issued, fully paid and nonassessable.

This opinion letter has been prepared for use in connection with the registration of the Preferred Shares pursuant to the Registration Statement. We assume no obligation to advise you of any changes in the foregoing subsequent to the registration of the Preferred Shares.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Current Report on Form 8-K related to the public offering of the Preferred Shares. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Securities Act of 1933, as amended.

Very truly yours,

/s/ HOGAN LOVELLS US LLP

HOGAN LOVELLS US LLP