An electronic device may have a conductive housing with an antenna window. A display cover layer may be mounted on the front face of the device. Antenna and proximity sensor structures may include a dielectric support structure with a notch. The antenna window may have a protruding portion that extends into the notch between the display cover layer and the antenna and proximity sensor structures. The antenna and proximity sensor structures may have an antenna feed that is coupled to a first conductive layer by a high pass circuit and capacitive proximity sensor circuitry that is coupled to the first conductive layer and a parallel second conductive layer by a low pass circuit. The first conductive layer may be formed from a metal coating on the support structure. The second conductive layer may be formed from patterned metal traces in a flexible printed circuit.