The magnetic levitation effect has been utilized to verify the superconductivity of thin (<2 mm), planar samples of YBaCuO. The levitation height obtained was much smaller than is predicted by simple theory, and the samples were not found to produce any discernible distortion of magnetic fields. This behaviour is modeled using an extended image system which allows for both sample thickness and a finite effective permeability. Predictions based on this model are compared with the observed behaviour and with published data. In addition to this, it was found that the properties of these samples were anisotropic, which could have implications for the processing of large samples of bulk ceramic superconductors.