EXHIBIT 99.1 CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002 (18 U.S.C. SECTION 1350) In connection with the accompanying Annual Report of Brigham Exploration Company (the "Company") on Form 10-K/A, Amendment No. 1, for the period ended December 31, 2002 (the "Report"), I, Ben M. Brigham, Chief Executive Officer, President and Chairman of the Board of the Company, hereby certify that: (1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and (2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company. Dated: June 10, 2003 /s/ Ben M. Brigham - ------------------ Ben M. Brigham Chief Executive Officer