Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER AND

CHIEF FINANCIAL OFFICER

Pursuant to 18 U.S.C. § 1350 and in connection with the accompanying report on Form 10-Q of Stone Energy Corporation (the “Company”) for the quarterly period ended September 30, 2012 that is being filed concurrently with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned officers of the Company hereby certifies, to the best of his knowledge, that:

(i.) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(ii.) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

November 6, 2012

/s/ David H. Welch

David H. Welch

President and Chief Executive Officer

/s/ Kenneth H. Beer

Kenneth H. Beer

Executive Vice President and Chief Financial Officer