Mechanically driven magnetoelectric (ME) antennas have been demonstrated to be one of the most effective methods to miniaturise antennas compared to state-of-the-art compact antennas. However, the nanoelectromechanical systems (NEMS) ME antennas are fragile due to their suspended thin-film heterostructure, and have very low power handling capabilities. Here we show that solidly mounted resonator (SMR)-based NEMS ME antennas on a Bragg acoustic resonator, which have a circular resonating disk of 200 μm diameters and operate at 1.75 GHz, show a high antenna gain of -18.8 dBi and 1dB compression point (P1dB) of 30.4 dBm. Compared to same-size thin-film bulk acoustic resonator (FBAR) ME antennas with a free-standing membrane, the SMR-based antennas are much more structurally stable with 23.3 dB higher power handling capability and easier fabrication steps. These SMR-based ME antennas are fabricated with processes compatible with complementary metal-oxide-semiconductor (CMOS), exhibiting dramatic size miniaturisation, high power handling, high mechanical robustness, simple fabrication processes, and much higher antenna radiation gain compared to same-size state-of-the-art antennas.