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,
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: May 11, 2005

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

      Dated: May 11, 2005

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