An electronic device may be provided with a housing, a logic board, and wireless circuitry on the logic board. The wireless circuitry may include first and second antennas formed from conductive traces on a surface of the logic board. The first and second antennas may include resonating element arms at opposing sides of the logic board. The first antenna may have a fundamental mode that radiates in a Bluetooth® communications band at 2.4 GHz. The second antenna may radiate in a first ultra-wideband communications band such as a 6.5 GHz ultra-wideband communications band. If desired, the second antenna may also radiate in a second ultra-wideband communications band such as an 8.0 GHz ultra-wideband communications band. In another suitable arrangement, a harmonic mode of the first antenna may radiate in the second ultra-wideband communications band.