Carbon capture storage and/or utilization (CCUS) is a viable option to meet decarbonization targets while still utilizing conventional fuel combustion for power generation. A significant portion of the captured CO2 will be transported to storage or processing facilities by ships. The overall design of a CO2 carrier and required tank capacity are influenced by its role within the carbon capture and storage (CCS) value chain. Tank design challenges arise from material selection, storage pressure, size, arrangement constraints and fatigue of structural elements. Cryogenic CO2 storage is also affected by the boil off rates, CO2 purity and margin availability from the triple point to avoid ice formation. Tank characteristics will determine the ship main dimensions and the required cargo handling machinery. In this work a thermodynamic model is employed to analyse the behaviour of cryogenic pressurized CO2 tanks, offering model-based insights into the influence of tank design features, processes, and phenomena relevant to the marine transportation of liquefied CO2. The model was used to investigate the impact of tank dimensions and insulation on the tank pressure accumulation profile. Operational scenarios were simulated to explore pressure management strategies during voyage conditions, including tank loading, unloading and spray cooling. The findings provide valuable insight to designers and operators by highlighting the behaviour and limitations associated with managing CO2 cargo under cryogenic conditions during marine transportation.