The incomplete description of the subsurface processes by physically-based groundwater models often results in biased and correlated prediction errors, thus suggesting the need for systematic correction of errors before conducting prediction uncertainty analysis. In this work, error-mapping artificial neural networks (ANN) are used to correct the physically-based groundwater model (MODFLOW) prediction errors. The resulting prediction uncertainty of the coupled MODFLOW-ANN model is then assessed using three alternative methods. The first method establishes approximate confidence and prediction intervals using first-order least-squares regression approximation (also called first-order error analysis). The second method employs bootstrap approaches that involve resampling of the uncertain data with replacement and repeated model runs for constructing the confidence and prediction intervals. The third method relies on a Bayesian approach that uses analytical or Monte Carlo methods to derive the posterior distribution. The performance of these approaches is evaluated using a hypothetical case study developed based on a phytoremediation site at the Argonne National Laboratory, USA. The results indicate that the three approaches yield comparable confidence and prediction intervals, thus making the computationally efficient first-order error analysis approach attractive for estimating the coupled model uncertainty. The results also demonstrate that the error-mapping ANN not only captures some of the local biases in the MODFLOW prediction, but also systematically reduces the prediction variance.