Exhibit 32(b)

Certification Pursuant to 18 U.S.C. Section 1350

I, Mark J. Plush, Vice President and Chief Financial Officer of Keithley Instruments, Inc. (the “Company”), certify, pursuant to 18 U.S.C. Section 1350, that:

(1) The Annual Report on Form 10-K of the Company for the period ended September 30, 2004 which this certification accompanies fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Mark J. Plush

Mark J. Plush

Vice President and Chief Financial Officer

December 13, 2004

A signed original of this written statement has been provided to Keithley Instruments, Inc. and will be retained by Keithley Instruments, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.