The axion is a hypothetical particle which is a candidate for cold dark matter. Haloscope experiments directly search for these particles in strong magnetic fields with RF cavities as detectors. The Relic Axion Detector Exploratory Setup (RADES) at CERN in particular is searching for axion dark matter in a mass range above 30 <inline-formula><tex-math notation="LaTeX">\mu</tex-math></inline-formula>eV. The figure of merit of our detector depends linearly on the quality factor of the cavity and therefore we are researching the possibility of coating our cavities with different superconducting materials to increase the quality factor. Since the experiment operates in strong magnetic fields of 11 T and more, superconductors with high critical magnetic fields are necessary. Suitable materials for this application are for example REBa<inline-formula><tex-math notation="LaTeX">_2</tex-math></inline-formula>Cu<inline-formula><tex-math notation="LaTeX">_3</tex-math></inline-formula>O<inline-formula><tex-math notation="LaTeX">_{7-x}</tex-math></inline-formula>, Nb<inline-formula><tex-math notation="LaTeX">_3</tex-math></inline-formula>Sn or NbN. We designed a microwave cavity which resonates at around 9 GHz, with a geometry optimized to facilitate superconducting coating and designed to fit in the bore of available high-field accelerator magnets at CERN. Several prototypes of this cavity were coated with different superconducting materials, employing different coating techniques. These prototypes were characterized in strong magnetic fields at 4.2 K.