The present invention pertains to an apparatus and method for conducting magnetic resonance measurements on fluids at high pressures and/or high temperatures. The apparatus can be used in conjunction with or as part of a downhole fluid sampling tool to perform NMR measurements on fluids withdrawn from petroleum reservoirs, or can also be used for laboratory measurements on live reservoir fluids. The apparatus can perform all of the measurements made by modern NMR logging tools, including multi-dimensional distribution functions of spin-spin (T2) and spin-lattice relaxation (T1) times and molecular diffusion coefficients. The spin densities of hydrogen and other NMR sensitive species can be computed from the distribution functions. The apparatus can also be used to predict the apparent conductivity of the fluids in the flowline from measurements of the quality factor (“Q”) of the NMR circuit. The apparent conductivity can be used to predict water cut or water salinity.