Stone Energy (SGY) 10-Q 2004 Q3 Quarterly report

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 for the quarterly period ended September 30, 2004 that is being filed concurrently with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned officers of Stone Energy Corporation (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 8, 2004

        /s/ David H. Welch      
  David H. Welch
  President and Chief Executive Officer

        /s/ James H. Prince      
  James H. Prince
  Executive Vice President and Chief Financial Officer