We consider a system where a spherical particle is suspended in a nematic liquid crystal confined between two walls. We calculate the liquid-crystal-mediated potential of mean force between the sphere and a substrate by means of Monte Carlo simulations. Three methods are used: a traditional Monte Carlo approach, umbrella sampling, and a novel technique that combines canonical expanded ensemble simulations with a recently proposed density-of-states formalism. The latter method offers advantages in that it facilitates good sampling of phase space without prior knowledge of the energy landscape of the system. The resulting potential of mean force, computed as a function of the normal distance between the sphere and a surface, suggests that the sphere is attracted to the surface, even in the absence of attractive molecular interactions.