Josephson junctions provide a useful means to observe nonlinear systems and macro-scale quantum interaction.  We would be able to observe previously unstudied phenomena if we could send 10 to 40 GHz microwave signals, with a constant power, to Josephson junctions in a cryostat.  However, putting Josephson junctions in a cryostat requires surrounding them by a metal box for electromagnetic shielding and heat dissipation reasons.  Resonance can occur in this metal box, and the resulting power spikes prevent us from    measuring a reliable output.  To better understand how this resonance behaves, we measure the resonant frequencies, between 8 and 12.5 GHz, of four copper cavities between 1.8 and 5.3 cm in length.  We find that the Q of the peaks in all cases is lower than expected and that the entire circuit, and not just the cavity, resonates.  We also find that the effective length of the cavity with respect to its resonant frequency is reduced by the introduction of two nuts inside the cavity.  We discuss the implications of these findings for future   experiments involving high frequency signals sent to Josephson junctions.