The CERN Resonant Weakly Interacting sub-eV Particle Search probes the existence of weakly interacting sub-eV particles like axions or hidden sector photons. It is based on the principle of an optical light shining through the wall experiment, adapted to microwaves. Critical aspects of the experiment are electromagnetic shielding, design and operation of low loss cavity resonators, and the detection of weak sinusoidal microwave signals. Lower bounds are set on the coupling constant g ¼ 4:5 Â 10 À8 GeV À1 for axionlike particles with a mass of m a ¼ 7:2 eV. For hidden sector photons, lower bounds are set for the coupling constant ¼ 4:1 Â 10 À9 at a mass of m 0 ¼ 10:8 eV. For the latter we are probing a previously unexplored region in the parameter space.