An electronic device may include wireless circuitry having a set of two or more antennas coupled to voltage standing wave ratio (VSWR) sensors. The VSWR sensors may gather VSWR measurements from radio-frequency signals transmitted using the set of antennas. The antennas may be disposed on one or more substrates and/or may be formed from conductive portions of a housing. Control circuitry may process the VSWR measurements to identify the ranges between each of the antennas in the set of antennas and an external object. The control circuitry may process the ranges to identify an angular location of the external object with respect to the device. The control circuitry may adjust subsequent communications based, adjust the direction of a signal beam produced by a phased antenna array, identify a user input, or perform any other desired operations based on the angular location.