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, 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: August 11, 2004

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

      Dated: August 11, 2004

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