Consider state estimation in a nonlinear or non-Gaussian state-space model. We compute confidence regions for the state estimation error of nonlinear filters, especially the extended Kalman filter, in nonlinear discrete-time state-space models. After analyzing the filtering error dynamics, a surrogate error process is constructed, whose quantiles can be easily computed. Then, it is shown that under some conditions, we may use the quantiles of the surrogate distribution to compute component-wise confidence intervals for the true estimation error of the nonlinear filtering algorithms. The above surrogate approach applies in nonlinear systems with Gaussian and non-Gaussian noises. The derived confidence intervals are expected to be sharper (smaller) than those derived from moment-based probability inequalities such as the Chebyshev and the Chernoff bounds.