EXHIBIT 32.1

CONTANGO OIL & GAS COMPANY

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Contango Oil & Gas Company (the “Company”) on Form 10-K for the year ended June 30, 2004 (the “Report”), as filed with the Securities and Exchange Commission on the date hereof, I, Kenneth R. Peak, Chairman, Chief Executive Officer and Chief Financial Officer of the Company, hereby certify, to my knowledge, that:

1. The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

Dated: September 27, 2004

/s/ KENNETH R. PEAK

Kenneth R. Peak

Chairman, Chief Executive Officer and Chief Financial Officer