Scanning near-field optical microscopy has been recently applied to the imaging of magnetic samples. It was shown experimentally that an apertureless microscope suffers a substantial loss of resolution when used for magneto-optical imaging compared with that for conventional imaging. No such change is observed for aperture microscopes. We explain this observation by developing a model for the imaging process that incorporates the response of the probe. We calculate real observable properties such as the rotation of polarization at the detector or the circular dichroism signal and thus simulate magneto-optical images of a domain structure in cobalt for both aperture and apertureless microscopes.