EXHIBIT 32.1

                                  CERTIFICATION

      PURSUANT TO 18 U.S.C SECTION 1350 AS ADOPTED PURSUANT TO SECTION 906
                        OF THE SARBANES-OXLEY ACT OF 2002

         Pursuant to 18 U.S.C. Section 1350 as adopted pursuant to Section 906
of the Sarbanes-Oxley Act of 2002, each of the undersigned officers of Rand
Capital Corporation (the "Company"), does hereby certify, to such officer's
knowledge, that:

         The Quarterly Report on Form 10-Q for the quarter ended March 31, 2004
(the Form 10-Q) of the Company fully complies with the requirement of section
13(a) or 15(d) of the Securities Exchange Act of 1934 and the information
contained in the Form 10-Q fairly presents, in all material respects, the
financial condition and results of operations of the Company.

    Dated: May 13, 2004

                                                   /s/ Allen F. Grum
                                        ----------------------------------------
                                                Allen F. Grum, President
                                               (Chief Executive Officer)

    Dated: May 13, 2004

                                                /s/ Daniel P. Penberthy
                                        ----------------------------------------
                                             Daniel P. Penberthy, Treasurer
                                               (Chief Financial Officer)