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We have developed a high resolution optical technique to measure the electromechanical properties of MEMS microstructures. The technique is applied to microbridges developed for capacitive switching in coplanar radio frequency (RF) waveguides. The thin metal ground plane on the substrate and the bottom of the bridge together form a microcavity for an optical beam. The wavelength of a cavity mode is a sensitive measure of the bridge position relative to the substrate. The technique is applied to the measurement of resonances and damping times of microbridges of varying lengths. It is also used to measure dc changes in bridge height of tenths of nanometers, driven ac displacements of less than a picometer, and bridge displacement noise of hundreds of femtometers per root Hertz. This extreme sensitivity exceeds previously demonstrated optical characterization methods.