EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The undersigned, Richard J. Campo, Chairman of the Board and Chief Executive Officer of Camden Property Trust (the “Company”), and Alexander J. Jessett, the Senior Vice President-Finance, Chief Financial Officer and Treasurer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that:

1. The Quarterly Report on Form 10-Q of the Company for the period ended June 30, 2013 (the “Report”) fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in Quarterly Report on Form 10-Q fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/Richard J. Campo

Richard J. Campo

Chairman of the Board of Trust Managers and

Chief Executive Officer

/s/Alexander J. Jessett

Alexander J. Jessett

Senior Vice President-Finance,

Chief Financial Officer and Treasurer

July 26, 2013