Accurate intermolecular potentials are needed for quantitative molecular simulations, but their calculation from quantum mechanics can be very demanding. We have developed several variations of a procedure, which we collectively refer to as quantum mechanical Hybrid Methods for Interaction Energies (HM-IE), to accurately estimate interaction energies from CCSD(T) calculations with a large basis set (LBS). HM-IE was tested for interaction energies of Ne-2, (C2H2)(2), and N-2-benzene for many orientations sampling the entire potential energy surface and was found to be in excellent agreement with the CCSD(T)/LBS results while requiring considerably less computational time and resources. Furthermore, for neon, an intermolecular potential fit to interaction energies using HM-IE and a potential fit to CCSD(T)/LBS energies resulted in nearly identical predictions for densities and vapor pressures.