Proton relaxation rates of nematic liquid crystals confined in nanoporous cavities were measured in a broad frequency range with the help of field cycling nuclear magnetic resonance relaxometry. The shape of relaxation dispersion curves in confined materials strongly deviates from the behavior in bulk, both above and below the bulk isotropization temperature. A strong increase in relaxation rates, exceeding by two orders of magnitude that of the bulk sample, is observed in the range of a few kilohertz. Relaxation rates in bigger pores decreased. Experimental findings are interpreted in terms of surface-induced orientational order and diffusion between sites with different orientations of local directors. With the aid of Monte Carlo simulations, two processes affecting low-frequency relaxation could be identified: (a) exchange losses of molecules from the surface-ordered phase to the bulk-like phase, and (b) Reorientations Mediated by Translational Displacements, which dominate the long-time scale and account for the recovery of correlation in molecular orientations as molecules probe different surface sites. It is shown that the width of the oriented layer may strongly affect the slope of dispersion curves and that cross-over between plateau and power law dispersion regimes shifts towards lower frequencies for bigger pores.