EXHIBIT 99(a) SECTION 906 CERTIFICATION BY THE CHIEF EXECUTIVE OFFICER I, Timothy W. Byrne, Chief Executive Officer of United States Lime & Minerals, Inc. (the "Company"), hereby certify that, to my knowledge: (1) The Company's periodic report on Form 10-K for the year ended December 31, 2002 (the "Form 10-K") 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 Form 10-K fairly presents, in all material respects, the financial condition and results of operations of the Company. Dated: March 27, 2003 /s/ Timothy W. Byrne -------------------------- Timothy W. Byrne