Saddlepoint techniques provide numerically accurate, higher-order, small sample approximations to the distribution of estimators and test statistics. While a rich theory is available for saddlepoint approximations in the setting of independently and identically distributed data, only a few results are available for dependent data. In this talk, we explain how to fill this gap in the literature: using the method of the tilted-Edgeworth expansion, we derive saddlepoint density approximations and saddlepoint test statistics when data are characterized by spatial or temporal correlation. We focus on panel data models with spatially correlated errors and on time series models. Our novel techniques can be helpful in both theory and practice. For instance, they define new tools for the theoretical analysis of inferential procedures on stochastic processes– e.g., in the approximation of the estimator bias in finite samples–and they are useful devices for the practical implementation of inferential procedures—e.g., for the approximation of p-values in real data applications. We compare our new approximations to the ones obtained by standard first-order asymptotic theory, by Edgeworth expansion and by resampling methods. The numerical exercises illustrate that our approximations yield accuracy’s improvements, while preserving analytical tractability.