Artificial neural networks have proven to be superior prediction models in many hydrology-related areas; however, failure of ANN practitioners to account for uncertainty in the predictions has limited the wider use of ANNs as forecasting models. Conventional methods for quantifying parameter uncertainty are difficult to apply to ANN weights because of the complexity of these models, and complicated methods developed for this purpose have been not been adopted by water resources practitioners because of the difficulty in implementing them. This paper presents a relatively straightforward Bayesian training method that enables weight uncertainty to be accounted for in ANN predictions. The method is applied to a salinity forecasting case study, and the resulting ANN is shown to significantly outperform an ANN developed using standard approaches in a real-time forecasting scenario. Moreover, the Bayesian approach produces prediction limits that indicate the level of uncertainty in the predictions, which is extremely important if forecasts are to be used with confidence in water resources applications.