  We propose and demonstrate a general method to calibrate the
frequency-dependent response of self-compensating noble-gas-alkali-metal
comagnetometers to arbitrary spin perturbations. This includes magnetic and
nonmagnetic perturbations like rotations and exotic spin interactions. The
method is based on a fit of the magnetic field response to an analytical model.
The frequency-dependent response of the comagnetometer to arbitrary spin
perturbations can be inferred using the fit parameters. We demonstrate the
effectiveness of this method by comparing the inferred rotation response to an
experimental measurement of the rotation response. Our results show that
experiments relying on zero-frequency calibration of the comagnetometer
response can over- or under-estimate the comagnetometer sensitivity by orders
of magnitude over a wide frequency range. Moreover, this discrepancy
accumulates over time as operational parameters tend to drift during
comagnetometer operation. The demonstrated calibration protocol enables
accurate prediction and control of comagnetometer sensitivity to, for example,
ultralight bosonic dark-matter fields coupling to electron or nuclear spins as
well as accurate monitoring and control of the relevant system parameters.
