In cavity-based optomechanical platforms, the coupling between the optical modes of a cavity and the vibrational modes of a mechanical resonator is mediated by radiation pressure. High contrast gratings (HCGs) have attracted a lot of interest for such platforms because they offer a way to make high reflectivity (> 99.5%), low mass mirrors. In its simplest form, a high contrast grating is a high index dielectric slab that has been patterned with sub-wavelength scale features to create a periodic modulation of the refractive index in one or two dimensions. Optomechanical platforms also need these low mass reflectors to act as mechanical resonators with a high mechanical quality factor Q. Stressed silicon nitride on silicon has emerged as a leading candidate for such devices because these films possess mechanical quality factors in excess of 10^5. Due to the stress that these silicon nitride films are under, 2D HCGs end up being more tolerant of the microfabrication process than their 1D counterparts. Additionally, those based on a symmetric 2D photonic crystal lattice are expected to be insensitive to the polarization of light at normal incidence. This thesis looks at the performance of 2D silicon nitride HCGs, as well as examines some of the properties of stressed silicon nitride films that limit their performance. We present a new method to separate transmission losses from dissipative losses in an HCG and find that dissipative losses are not the dominant factor in limiting the reflectivity of 2D HCGs. Our results also show that a slight anisotropy in the refractive index of stressed silicon nitride films can make these HCGs birefringent, thereby breaking the degeneracy between polarization eigenmodes when the HCGs are used as the end mirror in an optical cavity.