We demonstrate micromechanical reflectors with a reflectivity as large as 99.4% and a mechanical quality factor Q as large as 7.8 × 105 for optomechanical applications. The reflectors are silicon nitride membranes patterned with sub-wavelength grating structures, obviating the need for the many dielectric layers used in conventional mirrors. We have employed the reflectors in the construction of a Fabry-Perot cavity with a finesse as high as F = 1200, and used the optical response to probe the mechanical properties of the membrane.