The volume current method is used to estimate analytically the scattering losses that are due to boundary corrugations and surface roughness in microdisk and ring resonators. The harmonic components of boundary imperfections either phase match the unguided continuum or lead to tunneling radiation. Phase-matched radiation can contribute significant loss and is only weakly dependent on disk radius. In high-index contrast devices the longitudinal electric field component is thus responsible for most of the radiation.