Hamiltonian Truncation is a promising numerical approach for performing calculations in quantum systems nonperturbatively. In this talk, we outline a procedure for applying Hamiltonian Truncation in the case of Quantum Field Theories (QFTs) that have UV divergences. We first review Hamiltonian Truncation and its application to QFTs defined as conformal field theories deformed with relevant operators. We then analyse the UV divergences using perturbation theory, explain our procedure for removing UV divergences, and finally demonstrate it in some example nonperturbative numerical calculations.