An electronic device may be provided with wireless circuitry. Control circuitry may be used to adjust transmit power levels for wireless signals, may be used to tune antennas, and may be used to adjust other settings for the wireless circuitry. The electronic device may have a coupler interposed between an antenna and wireless transceiver circuitry. The coupler and a receiver within the transceiver circuitry may be used to make measurements on tapped antenna signals such as transmitted signals and signals reflected from the antenna. By analyzing the tapped antenna signals, S-parameter phase and magnitude information may be gathered that provides insight into whether the electronic device is operating properly and whether an external object is adjacent to the antenna. If an external object is present, the electronic device may limit wireless transmit power and may adjust tunable components in the antenna to compensate for detuning from the external object.