Naval vessels around the world are looking to reduce their fuel consumption to not only drive down their environmental impact, but also gain the additional benefit of improving their endurance and reducing their (strategic) dependency on their primary fuel sources. Therefore, based on the strategic value of fuel in the operational environment, multiple navies around the world are investigating alternative energy conversion devices and fuels. In recent years, solid oxide fuel cells (SOFCs) have gathered increasing attention for maritime applications as an alternative to the traditional diesel engines. SOFCs showcase high power generation efficiency, ultralow emissions and noise-free operation, which are ideal pre-requisites for power generation onboard naval and commercial ships. Capitalizing on these attributes of SOFCs, this paper aims to investigate the potential of a novel COmbined drive of Fuel cell And Internal Combustion Engine (COFAICE) for naval vessels that employs a SOFC-ICE integration concept for power generation. In this paper, the performance of SOFC-ICE integration is tested for three different case studies of naval ships, namely, an oceangoing patrol vessel, a landing platform dock and a high-speed surface combatant. We investigate the optimal load sharing between the two energy conversion devices for different operational profiles and operating modes of a notional naval vessel. Optimal load sharing strategies are generated to study the impact on power-generation efficiency and CO2 emissions while taking into account the space and weight considerations for the system and fuel bunkering. The performance of the natural gas-fuelled SOFC-ICE integration concept is compared against the conventional and existing power plants onboard comparable ships. Furthermore, based on the optimal power split, potential of two SOFC-ICE integration methods are investigated for part-load operations. We find that significant improvements in efficiency and CO2 emission reductions can be achieved for the integrated SOFC-ICE power plants with optimized space and weight considerations.