The possibility of using very‐high‐Qsuperconducting microwave cavities to obtain a strong coupling between the electromagnetic field and a Josephson junction has prompted a study of such systems. Expressions have been obtained describing the dcI‐Vcharacteristic of a junction biased so that the Josephson radiation frequency is near a resonance of the cavity in which it is located. The rf power coupled into anX‐band (10 GHz) TE011mode cavity from a weakly coupled junction is approximately3×10−13 I02 Q W, whereI0is the critical current of the junction andQis the cavityQ. When the coupling between the junction and cavity is large enough, theI‐Vcharacteristic becomes multiple valued and the power coupled to the cavity depends on the state of the system. The maximum power which can be coupled to the cavity is approximately 0.58I0Vdc, whereVdcis the voltage required to bias the junction to the resonant frequency of the cavity.