The spin-rotational levels of FeH in its F4Δ and X4Δ states are significantly perturbed by nearby electronic states. As a result, it is not possible to make reliable calculations of its magnetic dipole moments from a simple effective Hamiltonian. In this paper, we report experimental measurements of the magnetic dipole moments of FeH in several rotational levels of the two lowest spin components of the v = 0 levels of both the F4Δ and X4Δ states. The observational data are taken from the Sunspot Spectral Atlas of Wallace et al.; the local magnetic flux densities are determined from the splittings of atomic lines present in the spectrum. These results considerably extend the range of known magnetic dipole moments for FeH and provide many lines in the F4Δ–X4Δ transition at 990 nm (the Wing-Ford system) for astronomers to use for the measurement of the local magnetic fields of cool stars where suitable atomic lines are not available for this purpose.