An experiment suitable for an advanced undergraduate laboratory is described in which the free−electron cyclotron resonance of electrons trapped in a microwave cavity by a Penning trap is observed. The systematic errors appear to be less than in the Gardner and Purcell cyclotron resonance experiment, amounting to not more than 20 ppm, probably less. The resonance peak can be located with a precision of 5 ppm with modest equipment. Since the microwave cavity is easy to construct, the experiment constitutes an attractive alternative to one of the Gardner−Purcell variety.