We give a detailed treatment of electromagnetic signals generated by gravitational waves (GWs) in resonant cavities. We show that it is crucial to carry out the signal calculation in a preferred frame for the laboratory, the proper detector frame. This formalism allows us to firmly establish that cavity experiments which were designed for the detection of axion dark matter can also search for high-frequency GWs. We also discuss several GW sources in the high-frequency regime such as the cosmic gravitational microwave background, GWs from superradiant boson clouds and inspiraling black holes. In the end we compare the signals strength of these sources with the the sensitivities of the resonant cavities.
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