The International Maritime Organization has set clear objectives towards drastically reducing greenhouse gas emissions the coming decades in the maritime sector. While different ways to reduce emissions are already proposed, these are not expected to generate high CO₂ abatement rates (in the case of fuel saving measures) or to be available and cost competitive in the near future (in the case of alternative fuels). Alternatively, ship-based carbon capture (SBCC) technology could be implemented on the shorter term and has the potential to drastically reduce the CO₂ emissions of the maritime sector. This study discusses the advancements made towards the SBCC technology on board of LNG-fuelled ships using the results of the DerisCO2 project. The study covers general design considerations for the SBCC technology (solvent selection, heat integration and effect of ship movement), next to specific design considerations for the Sleipnir ship of Heerema Marine Contractors (analysis of operational profile, conceptual design and high level integration of the SBCC system), which is used as a case study for SBCC in this paper. Simulation of the SBCC technology including a techno-economic analysis on the case studies are included. The SBCC technology is a technically and economically viable solution for the maritime sector to reduce emissions the coming decades, with the cost of CO₂ capture for the Sleipnir calculated between 119-133 €/ton CO₂. The most important proposed next step for fast development of the SBCC system is on board demonstration of the technology.