The aim of this paper is to propose a suitable method for constructing prediction intervals for the output of neural network models. To do this, we adapt the extremely randomized trees method originally developed for random forests to construct ensembles of neural networks. The extra-randomness introduced in the ensemble reduces the variance of the predictions and yields gains in out-of-sample accuracy. An extensive Monte Carlo simulation exercise shows the good performance of this novel method for constructing prediction intervals in terms of coverage probability and mean square prediction error. This approach is superior to state-of-the-art methods extant in the literature such as the widely used MC dropout and bootstrap procedures. The out-of-sample accuracy of the novel algorithm is further evaluated using experimental settings already adopted in the literature.