Epistemic uncertainties create difficulties for the quantitative estimation of uncertainties associated with environmental models. The nature of the issues involved is discussed, particularly in how to assign likelihood values to models when the forcing data and evaluation data might both be subject to epistemic uncertainties. A case study of a rainfall-runoff model of the River Brue catchment is developed with the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. Model evaluation is carried out using limits of acceptability set from considerations of the available data prior to running a model, while the errors associated with a model are treated non-parametrically for different parts of the hydrograph.