This work presents a general scheme for constructing pseudopotentials for advanced density functional theory (DFT) calculations employing range-separated hybrid (RSH) functionals. The authors demonstrate pseudopotential construction for several atoms and RSH functionals, and find that pseudopotential consistency errors tend to be systematic when computing solid-state properties and can exceed 0.1 eV for band gaps. This work removes the need to incur such unnecessary errors when performing state-of-the-art electronic structure calculations at the computationally demanding RSH-DFT level.