The damage fluences of gratings for diffraction of ultraviolet radiation, which are used in high-order harmonic generation experiments, have been measured with respect to the fundamental laser beam radiation. We have tested gold and platinum coatings of 40- and 50-nm thickness, respectively, deposited onto fused-silica substrates, after irradiation of high-energy, spatially filtered, 20-fs laser pulses at 780 nm. The damage appears at a fluence of approximately 0.3 J cm(-2) for gold and at a fluence of approximately 0.4 J cm(-2) for platinum. Scanning electron microscopy of the irradiated regions revealed different damaging mechanisms for the two coatings.