Long-range marine transportation is crucial for the global economy, and the carbon dioxide (CO₂) released by this industry contributes about 3% of global man-made CO₂ emissions. Capturing CO₂ directly from engine exhaust and storing it onboard is a promising solution to decarbonize the marine transport industry. New regulations aimed at reducing greenhouse gas emissions have spurred a wave of technological developments focused on onboard carbon capture technologies. In this paper, we present a novel conceptual design for an onboard carbon capture and storage system mainly utilizing a new generation of polymeric CO₂-removal membranes. This system has been developed, modeled, and virtually demonstrated using a commercial process simulator. Additionally, we have compared our system with an amine-based onboard carbon capture and storage system, under various exhaust scenarios induced by different ship engine loads. Simulation results indicate that the membrane-based carbon capture and storage system significantly outperforms the amine-based carbon capture and storage system in both economic and environmental performance.