Solid oxide fuel cell (SOFC) technology offers a promising way to reduce maritime greenhouse gas (GHG) emissions.Integration with a proton exchange membrane fuel cell (PEMFC) allows unreacted hydrogen, produced in the SOFC stack, to be reused and increase the electrical efficiency of the system. In this study, the Cycle Tempo software is used to model a SOFC-PEFMC combined cycle system operating on methane. The system is thermodynamically analysed to reveal the influence of SOFC fuel utilisation, cell voltage, operating temperature and PEMFC cell voltage on the system performance. A multivariable parametric analysis is applied to generate contour plots of net electrical efficiency and fraction of total power produced by the PEMFC. The analysis shows that increasing the cell voltage of both the SOFC and PEMFC has a positive influence on efficiency, whereas increasing the fuel utilisation reduces the system efficiency. Efficiencies in the range of 50-68% can be achieved. Model assumptions for PEMFC operating parameters are verified to exert little influence on the system efficiency, which confirms the assumption of constant values for these parameters. This study highlights the high-efficiency potential of the combined system and the difficulties that arise from thermally integrating an SOFC with a PEMFC.