An electronic device may be provided with an antenna and transceiver circuitry such as millimeter wave transceiver circuitry. The antenna may include an antenna ground and a resonating element. The resonating element may include a cross-shaped patch having arms extending along different longitudinal axes, conductive landing pads interposed between the cross-shaped patch and the antenna ground, and vertical conductive legs extending between each of the arms and corresponding landing pads. The antenna may be fed using a first antenna feed coupled between a first of the landing pads and the antenna ground and a second antenna feed coupled between a second of the landing pads and the antenna ground. The landing pads, antenna ground, and cross-shaped patch may be formed from conductive traces on different layers of a dielectric substrate.