Detailed physics-based computer models of fuel cells can be computationally prohibitive for certain applications, including optimization, sensitivity analysis, uncertainty quantification and real-time control. Such applications can require an enormous number of runs in order to extract reliable results. Approximate models based on spatial homogeneity or data-driven techniques can serve as surrogates when scalar quantities such as the cell voltage are of interest. When more detailed information is required, e.g., the potential or temperature field, computationally inexpensive surrogate models are difficult to construct. In this paper we use dimensionality reduction to develop a surrogate model approach for high-fidelity fuel cell codes in cases where the target is a field. A detailed 3-d model of a high-temperature PEM fuel cell is used to test the approach. We develop a framework for using such surrogate models to quantify the uncertainty in a scalar/functional output, using the field output results. We propose a number of alternative methods including a semi-analytical approach requiring only limited computational resources.