  We identify the molecular ion NH^+ as a potential candidate for probing
variations in the fine structure constant alpha and electron-to-proton mass
ratio mu. NH^+ has an anomalously low-lying excited Sigma state, being only a
few hundred cm^-1 above the ground Pi state. Being a light molecule, this
proximity is such that rotational levels of the respective states are highly
intermixed for low angular momenta. We find that several low-frequency
transitions within the collective rotational spectrum experience enhanced
sensitivity to alpha- and mu-variation. This is attributable to the close
proximity of the Pi and Sigma states, as well as the ensuing strong spin-orbit
coupling between them. Suggestions that NH^+ may exist in interstellar space
and recent predictions that trapped-ion precision spectroscopy will be
adaptable to molecular ions make NH^+ a promising system for future
astrophysical and laboratory studies of alpha- and mu-variation.
