A continuum theory is used to study the interactions between nanoparticles suspended in nematic liquid crystals. The free energy functional that describes the system is minimized using an Euler-Lagrange approach and an unsymmetric radial basis function method. It is shown that nanoparticle liquid-crystal mediated interactions can be controlled over a large range of magnitudes through changes of the anchoring energy and the particle diameter. The results presented in this work serve to reconcile past discrepancies between theoretical predictions and experimental observations, and suggest intriguing possibilities for directed nanoparticle self-assembly in liquid crystalline media.