An electronic device may be provided with a primary antenna that is used for transmitting and receiving signals and a secondary antenna that is used for receiving signals. The primary and secondary antennas may be used together in a diversity arrangement when receiving signals. The electronic device may have a transceiver. A phase shifter may be interposed between the transceiver and the secondary antenna. Control circuitry may select a communications band of interest for transmitting signals with the primary antenna. The control circuitry can adjust the phase shifter in real time based on which communications band of interest has been selected for transmission with the primary antenna. The phase shifter may impose a phase shift on signals carried between the secondary antenna and the transceiver that ensures that primary antenna efficiency degradation associated with the presence of the secondary antenna in the vicinity of the primary antenna is avoided.