Cu/Me multilayer systems, with Me referring to a body-centered cubic () metal, such as Nb and W, are widely used for nuclear, electrical, and electronic applications. Despite making up only a small percentage of the volume, interfaces in such systems play a major role in determining their electrical, mechanical, thermal and diffusive properties. Face-centered cubic () Cu often forms Kurdjumov-Sachs (KS) and Nishiyama-Wassermann (NW) type interfaces with metals or variations thereof. For the Cu/Nb system, these interface relationships have been extensively studied with semi-empirical methods. Surprisingly, the energetics and interface properties of Cu/W have not yet been studied in detail, in spite of extensive applications. In this study, we employ both periodic Embedded Atom Method (EAM) and Density Functional Theory (DFT) simulations to explore the geometric and energetic properties of the KS and NW interfaces of Cu/Nb and Cu/W. To assess the reliability of our approach, the dependence of the results on the size of periodic cells is examined for coherent and incoherent interfaces. We provide the interface energies and the work of separation for the Cu/W and Cu/Nb interfaces at DFT accuracy. The results of calculations with two EAM potentials are in qualitative agreement with those obtained using DFT and allow investigating the convergence of interfacial properties. These key energetic quantities can be used for future thermodynamic and mechanical modeling of Cu/Me interfaces.