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Micromechanical resonators with resonant frequencies from 500 kHz to 10 MHz were built and examined for several energy loss mechanisms. Thermoelastic damping, clamping loss and air damping were considered. The devices were shown to be limited by thermoelastic damping, providing experimental verification of this phenomenon at the microscale. Resonators with scaled dimensions also matched well with scaling theory of damping at a given pressure. An energy loss mechanism other than thermoelastic dissipation, most likely clamping loss, was shown to be dominant for resonators whose ratio of length to width was less than 10:1. The devices were fabricated using a single-wafer encapsulation process.