Marine pollution is a major concern but one that has to date been largely overlooked; thus, for example, it was not accounted for in the Paris agreement on climate change. Maritime fuel combustion currently contributes 3% of the annual global greenhouse gas emissions. Nearly all shipping-related emissions occur within 400 km of land and cause death and morbidity to millions of people. The initial greenhouse gas strategy on the reduction of carbon emissions to at least half of its 2008 levels by 2050, adopted by the International Maritime Organization, has the potential to spur innovations and alternative fuel, enabling the shipping industry to adapt to future challenges. Some zero-emission options such as the use of hydrogen and biofuels are considered potential strategies, but they lack the infrastructure capacity needed to meet the world's shipping demand. Liquefied natural gas (LNG) has gained substantial interest as a marine fuel because it can comply with the strictest environmental regulations currently in force, and it is often regarded as a future fuel as most newly constructed ships are built to run on it. Although the use of LNG leads to lower CO2 emissions compared to traditional heavy fuel oils (HFOs), there is still a need to consider further reduction. A solution which can be implemented is the use of an onboard capture system on ships, also known as ship-based carbon capture. In this study, a process and economic evaluation was carried out on a solvent-based postcombustion capture process for the energy system of a CO2 carrier. A rate-based model was developed, validated, and scaled up to process the flue gas from a Wartsila 9L46 DF marine diesel engine. Different modes of operation with respect to engine load and capture rate were analyzed in this study, and the capture cost was estimated. The cost of CO2 capture was used as an economic index for this study. It was observed via a sensitivity analysis that, at 90% capture rate, the cost of capture was at least $117/t. The effect of exhaust gas recycling was also explored, and this resulted in a considerable reduction in the capture cost. The exhaust gas waste heat was utilized and was adequate to supply the required energy needed by the reboiler at each capture rate examined. Also, for LNG-fueled CO2 ships, the cold energy obtained while converting the LNG to gas was utilized to liquefy the captured CO2 from the flue gas.