An intense beam of relativistic electrons (800 A, 6.7 MeV) has been bunched at 35 GHz by a free-electron laser, in which output power levels exceeding 100 MW were obtained. The beam was then extracted and transported through a resonant cavity, which was excited by its passage. Microwave power levels of 10 MW were extracted from the cavity, in reasonable agreement with the simple formula which relates power to known properties of both the beam and the cavity.