Although the complex Langevin method can solve the sign problem in simulations of theories with complex actions, the method will yield the wrong results if known validity conditions are not satisfied. We present a novel method to compute observables for a target ensemble by reweighting complex trajectories generated with the complex Langevin method for an auxiliary ensemble having itself a complex action. While it is imperative that the validity conditions be satisfied for the auxiliary ensemble, there are no such requirements for the target ensemble. This allows us to enlarge the applicability range of the complex Langevin method. We illustrate this at the hand of a one-dimensional partition function and two-dimensional strong-coupling QCD.