We propose the use of indirect inference estimation for inference in locally stationary models. We develop a local indirect inference algorithm and establish the asymptotic properties of the proposed estimator. Due to the nonparametric nature of the model under study, the resulting estimators display nonparametric rates of convergence and behavior. We validate our methodology via simulation studies in the confines of a locally stationary moving average model and a locally stationary multiplicative stochastic volatility model. An application of the methodology gives evidence of non-linear, time-varying volatility for monthly returns on the Fama-French portfolios.