Estimation of confidence intervals for neural network outputs is important when the uncertainty of a neural network system must be addressed for safety or reliability. This paper presents a new approach for estimating confidence intervals, which can help users validate neural network outputs. The estimation of confidence intervals, called error estimation by series association, is performed by a supplementary neural network trained to predict the error of the main neural network using input features and the output of the main network. The accuracy of this approach is shown using a simple nonlinear mapping and more complicated, realistic nuclear power plant fault diagnosis problems. The results demonstrate that the approach performs confidence estimation successfully.