We study the nonlinear Klein–Gordon (NLKG) equation on a manifold M in the nonrelativistic limit, namely as the speed of light c tends to infinity. In particular, we consider a higher-order normalized approximation of NLKG (which corresponds to the NLS at order 𝑟=1) and prove that when M is a smooth compact manifold or ℝ𝑑, the solution of the approximating equation approximates the solution of the NLKG locally uniformly in time. When 𝑀=ℝ𝑑, 𝑑≥2, we also prove that for 𝑟≥2 small radiation solutions of the order-r normalized equation approximate solutions of the nonlinear NLKG up to times of order 𝒪(𝑐2(𝑟−1)). We also prove a global existence result uniform with respect to c for the NLKG equation on ℝ3 with cubic nonlinearity for small initial data and Strichartz estimates for the Klein–Gordon equation with potential on ℝ3.