Sensitivity analysis (SA) and uncertainty quantification (UQ) are used to assess and improve engineering models. SA of fuel cell models can be challenging because of the large number of design parameters to optimize. Following the regular approach of manually testing the fuel cell outputs under changing each design parameter one at a time can be tedious. In this work, a framework of SA and UQ methods is applied with a purpose of efficiently analysing fuel cell models. The SA and UQ methods are also compared to increase the confidence in the results. In this methodology, all design parameters and their effects can be analysed in an integrated form, where model variance, sensitivity, linearity/nonlinearity, parameter interactions, and importance ranking can be assessed. This paper highlights and compares between local SA (one-at-a-time linear perturbation), parameter screening (Morris screening), variance decomposition (Sobol indices), and regression-based SA. For UQ, stochastic methods (Monte Carlo sampling) and deterministic methods (using SA profiles) are used. All methods are applied to solid oxide fuel cell (SOFC) to analyse the power output and system efficiency under 21 uncertain design parameters. Using different methods, the uncertainty in the SOFC responses (maximum power and efficiency) is about 11%, when the current density is about 13 200 A m(-2). In addition, analysis shows that operating temperature (T), length of grain contact (X), grain size (D-s), porosity (epsilon), and electrolyte thickness (L-e) contribute to more than 97% of the SOFC's maximum power variance, with individual contributions as follows: 63.3%, 13.1%, 12.5%, 5.4%, and 3.6%, respectively. The previous conclusions are subjective to the simplified SOFC model used in this study to demonstrate the methods. Benchmarking the UQ methods in capturing the response uncertainty and the SA methods in raking the design parameters demonstrate very good agreement between them. The methods applied in this paper can be used to achieve a comprehensive mathematical understanding of more advanced fuel cell or energy models, which can lead to better performance.