Broadband antennas and handheld electronic devices with broadband antennas are provided. A handheld electronic device may have a housing in which electrical components such as integrated circuits and a broadband antenna are mounted. The broadband antenna may have a ground element and a resonating element. The resonating element may have two arms of unequal length and may have a self-resonant element. The antenna may have a feed terminal connected to the self-resonant element and a ground terminal connected to the ground element. The self-resonant element may be near-field coupled to one of the arms of the resonating element. With one suitable arrangement, the self-resonant element may be formed using a conductive rectangular element that is not electrically shorted to the ground element or the arms of the resonating element. The antenna may operate over first and second frequency ranges of interest.