It is a direct consequence of the Einstein equivalence principle (EEP) that all atomic clocks will run at the same rate if situated at the same point in space-time. This prediction of a universal gravitational redshift is a property of any self-consistent metric theory of gravity1. The class of experiments considered here essentially involves a comparison of two clocks, one of which is a quartz crystal stabilized to a caesium-beam atomic frequency standard, and the other, more important for this discussion, is a NMR clock, for which the `ticks' are provided by the free precession of a sample of polarized nuclear spins in a stable and uniform magnetic field. Two experimental null results have been reported, one by Hughes2 and the other by Drever3. We point out that some measurements already exist for spin 1/2 systems which can put tighter limits on anisotropic precession frequencies than the Hughes-Drever results, and we suggest an experimental technique that should allow a further improvement in precision by up to six orders of magnitude. Apart from the interest to gravitation physics these results are also important for high precision metrology and the provision of standards of magnetic flux density and electric current.