Wireless portable electronic devices such as laptop computers are provided with cavity-backed monopole antennas. A wireless device may have a housing. Conductive portions of the housing such as a conductive outer metal layer and internal frame structures may form a cavity having conductive walls. An antenna resonating element structure may be formed from monopole antenna resonating element arms of dissimilar lengths. One of the arms may be straight and another of the arms may be implemented using a meandering path. The antenna resonating element may be mounted over the cavity to form a cavity-backed monopole antenna. A display within the device may be covered by a cover glass. An opaque bezel region around the periphery of the cover glass may cover the antenna and block it from view. The antenna resonating element arms may run parallel to the longitudinal axis of the cavity.