In this work, we investigate the issue of providing a statistical model for the response of a computer model-described nuclear engineering system, for use in uncertainty propagation. The motivation behind our approach is the need for providing an uncertainty assessment even in the circumstances where only a few samples are available. Building on our recent work in using a regression approach with derivative information for approximating the system response, we investigate the ability of a universal gradient-enhanced Kriging model to provide a means for inexpensive uncertainty quantification. The universal Kriging model can be viewed as a hybrid of polynomial regression and Gaussian process regression. For this model, the mean behavior of the surrogate is determined by a polynomial regression, and deviations from this mean are represented as a Gaussian process. Tests with explicit functions and nuclear engineering models show that the universal gradient-enhanced Kriging model provides a more accurate surrogate model than either regression or ordinary Kriging models. In addition, we investigate the ability of the Kriging model to provide error predictions and bounds for regression models.