Solid oxide fuel cell systems are considered for the power plant of ships, because of their high efficiency, low pollutant emissions, and fuel flexibility. This research compares the volume, mass, fuel consumption, and emissions of different hybrid power plants for cruise ships using solid oxide fuel cells, fuelled with marine gas oil and liquefied natural gas. A component sizing model allocates the installed power over the selected power plant components and determines their size and weight. The components and energy management strategy are simulated with a cruise ship for five years of operation. A simple method is implemented to estimate the degradation and its effect on component operation. The combined component sizing and time-domain model highlights the importance of dynamic simulation for battery sizing. The results show that using solid oxide fuel cells for the auxiliary consumers can reduce greenhouse gas emissions by 21% and pollutants by 38% to 46% with only 17.5% installed power, which has limited consequences for the cost and size of the power plant. With 31% installed power, the ship can operate in low-emission zones while reducing greenhouse gas emissions by 33% and pollutants by 60% to 70%. Performing all cruise operations requires 51% installed fuel cell power and reduces greenhouse gas emissions by 49% and pollutants by 94% to 96%. In conclusion, the study affirms that solid oxide fuel cell systems, with proper sizing and energy management, can be used to reduce shipping emissions and reach IMO's 30% GHG emission reduction target for 2030.