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This article proposes a Built-In Self-Test (BIST) method to accurately measure the combinatorial circuit delays on an FPGA. The flexibility of the on-chip clock generation capability found in modern FPGAs is employed to step through a range of frequencies until timing failure in the combinatorial circuit is detected. In this way, the delay of any combinatorial circuit can be determined with a timing resolution of the order of picoseconds. Parallel and optimized implementations of the method for self-characterization of the delay of all the LUTs on an FPGA are also proposed. The method was applied to Altera Cyclone II and III FPGAs . A complete self-characterization of LUTs on a Cyclone II was achieved in 2.5 seconds, utilizing only 13kbit of block RAM to store the results. More extensive tests were carried out on the Cyclone III and the delays of adder circuits and embedded multiplier blocks were successfully measured. This self-measurement method paves the way for matching timing requirements in designs to FPGAs as a means of combating the problem of process variations.