Antennas are provided for electronic devices such as portable computers. An electronic device may have a housing in which an antenna is mounted. The housing may be formed of conductive materials. A dielectric window may be mounted in the housing to allow radio-frequency signals to be transmitted from the antenna and to allow the antenna to receive radio-frequency signals. A proximity sensor adjacent to the dielectric window may be used in detecting external objects. The antenna may have an antenna resonating element that is mounted against an inner surface of a display cover glass layer. The antenna resonating element may be mounted to an upper surface of a plastic carrier. An electromagnetic shield may be mounted on a lower surface of the plastic carrier above the proximity sensor.