An initial study of the field dependence of 59Co nuclear magnetic resonance (NMR) has been undertaken for two Co/Cu(111) multilayer films grown by molecular beam epitaxy. The multilayer structure of the films was nominally identical, [Co(15 Å)/Cu(7 Å)]×20, however by growing the multilayers with similar structures on different buffer layers, Cu(200 Å) and Au(10 Å), saturation magnetoresistances ΔR/R of 4% and 22%, respectively, were obtained. The NMR signal in ferromagnetic materials arises due to the enhancement effect from the electronic magnetization. This enhancement effect is therefore a function of the domain structure and any external magnetic field. By applying a simple model of how the NMR enhancement factor varies with applied field, in the absence of a domain structure, the anisotropy fields at the interfaces and in the bulk were determined separately at T=4.2 K. These were then compared with the coercive field obtained from magnetization measurements. Our results show that at low temperature the anisotropy field at the interfaces is approximately equal to the coercivity obtained from magnetization measurements (260 Oe), while in the bulk the anisotropy field was found to be ∼550 Oe for the low magnetoresistance sample with ΔR/R=4%, and ∼1230 Oe for the high magnetoresistance sample with ΔR/R=22%.