The resonator-based magnetic field sensor system has an oscillatory member as resonator, means for driving an electrical current through said resonator such that its resonance frequency is altered by an external magnetic field to be measured (measurand), and means for detecting or measuring said altered resonance frequency. A secondary excitation of the resonator is effected to determine the said altered resonance frequency from which the measurand can be deduced. In the preferred embodiment, the secondary excitation is included in a closed loop, thus creating an oscillator vibrating at the altered resonance frequency. Though it is known to use the oscillation amplitude of a suitable resonator for this purpose, the novel sensor system identifies and/or measures the frequency (not the amplitude) of the oscillation, which is a function of the magnetic field to be measured.