In one embodiment, a magnetometer includes an electromechanical resonator coupled to a drive-and-detect (DD) circuit. The resonator has a deformable beam that is a part of a closed current path. By applying a periodic drive signal to a drive electrode located in proximity to the deformable beam, the DD circuit induces an oscillation of the beam. In the presence of a magnetic field, this oscillation changes the magnetic flux through the closed current path, thereby generating an oscillating electrical current in the path. Dissipation of this current due to resistive losses in the closed current path then dampens the oscillation of the deformable beam with a damping coefficient that depends on the magnetic-field strength. Using a sense electrode located in proximity to the deformable beam, the DD circuit detects the oscillation amplitude. Based on the detected amplitude, the DD circuit changes the frequency of the drive signal to find the resonant frequency. Since the resonant frequency depends on the damping coefficient, the magnetic-field strength can be deduced in a relatively straightforward manner from the resonant frequency.