Strict International Maritime Organization (IMO) rules enable ships to maximize fuel consumption and compliance with the climate. Cooling and heat-pumping technology powered by waste heat makes a substantial contribution to lowering ship gas emissions. This study explores, technically studies, and thermodynamically analyzes the efficiency of ongoing adsorption refrigeration and heating systems using a zeolite−water pair onboard a naval surface ship. An updated Dubin-in-Astakhov equation calculates the equilibrium adsorption potential of the operating pair used in the system. The coefficient of performance (COP) and specific cooling power (SCP)/specific heating power (SHP) values were between 0.109 and 0.384 and between 69.13 and 193.58 W kg−1 for cooling mode, and between 66.16 and 185.26 W kg−1 based on exhaust gas temperature and regeneration, respectively. Up to 27.64% and 52.91% met the cooling and heating load of the case vessel at a full load by the zeolite−water-adsorbed refrigeration/heat-pumping system. The COP of the heat pump and cooling systems was compared to that of adsorption cooling/heat pumps in the literature.