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 June 30,
2005 (the Form10-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: August 4, 2005

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

      Dated: August 4, 2005

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