This paper is devoted to rigorous electromagnetic diffraction analysis, in the near infrared, for micromechanical silicon interdigitated beam gratings with both lateral and vertical displacement of movable beams. In the wavelength-to-period ratio domain where the gratings support three diffraction orders, the specific designs of high-efficiency switches for polarized radiation, such as switches from a transmitter to a 1 x 3 transmission beamsplitter and from a retroreflector to an 1 x2 reflection beam divider, are presented. The possibility of light modulation, which follows from these designs, is discussed. The analysis with respect to wavelength, beam-width, beam-height, and incidence-angle variations shows a good tolerance of the devices' performance to spectral shifts and to fabrication and mounting errors. in addition, with the use of our software we simulated the diffraction efficiency versus displacement at a visible wavelength for a micromechanical grating reported in the literature. There is good agreement between theory and experiment.