  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 $\mu$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$_2$Cu$_3$O$_{7-x}$, Nb$_3$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.
