The stiff compromise between reliability and conductivity of copper interconnects used in sub-nanometer nodes has brought into focus the choice of encapsulation material. While reliability was the primary driver so far, herein, we investigate how electronic conductivity of Cu(111) thin films is influenced by the encapsulation material using density functional theory and Boltzmann transport equation. Atomically thin 2D materials, namely conducting graphene and insulating graphane both retain the conductivity of Cu films whereas partially hydrogenated graphene (HGr) results in reduction of surface density of states and a reduction in Cu film conductivity. Among transition metal elements, we find that atoms in Co encapsulation layer, which essentially act as magnetic impurities, serve as electron scattering centres resulting in a decrease in conductivity by at least 15% for 11 nm thick Cu film. On the other hand, Mo, Ta, and Ru have more favorable effect on conductivity when compared to Co. The cause of decrease in conductivity for Co and HGr is discussed by investigating the electronic band structure and density of states. Our DFT calculations suggest that pristine graphene sheet is a good encapsulation material for advanced Cu interconnects both from chemical protection and conductivity point of view.