We describe a system for the measurement of the surface resistance of high-T c superconductors (HTCSs) at 48 GHz as a function of the temperature, the external magnetic field and its orientation with respect to the crystallographic axes of the sample. The set-up is based upon a resonant cavity. Thin films, bulk ceramics and single crystals can be accommodated in the cavity. A geometry in which there is no c axis microwave current flow, or c axis microwave field penetration, is chosen, so that unwanted effects depending on the anisotropy of HTCSs are ruled out. Geometrical factors for samples smaller than the cavity endplate are calculated. Some measurements on HTCS thin films and single crystals are presented, as well as some of the items of physical information obtainable from the measurements.