Ultracold gases provide micrometer size samples whose sensitivity to external fields may be exploited in sensor applications. Bose-Einstein condensates of atomic gases have been demonstrated to perform excellently as magnetic field sensors in atom chips. Here we propose that condensates of fermions can be used for noninvasive sensing of time-dependent and static magnetic and electric fields, by utilizing the tunable energy gap in the excitation spectrum as a frequency filter. Perturbations by the field create collective excitations and quasiparticles. The latter requires the frequency of the perturbation to exceed the gap. The frequencies of the field may be selectively monitored from the amount of quasiparticles which is measurable, e.g., by rf spectroscopy. We analyze the method by calculating the density-density susceptibility and discuss its sensitivity and spatial resolution.