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We present measurements of superconducting tunnel junction (STJ) spectrometers optimized for extreme ultraviolet (EUV) energies, between 20-200 eV. The high count rates demands of astronomical applications, such as solar flare studies, uniquely suit STJs as compared to other cryogenic spectrometers. We have simulated EUV measurements with the technique of multiphoton absorption using a pulsed UV laser as a light source. We have demonstrated an energy resolution of 2.15 eV, close to the requirements of the applications. This resolution is limited by amplifier noise. We present predictions of improved resolution based on new amplifier designs.