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The high demand for natural gas (NG) worldwide has led to an increase in the size of the LNG carrier fleet. However, the heat losses from this type of ship’s engines are not properly managed, nor is the excess boil-off gas (BOG) effectively utilised when generation exceeds the ship’s power demand, resulting in significant energy losses dissipated into the environment. This article suggests storing the lost energy into green H₂ for subsequent use. This work compares three different electrolysis technologies: solid oxide (SOEC), proton exchange membrane (PEME), and alkaline (AE). The energy required by the electrolysis processes is supplied by both the LNG’s excess BOG and engine waste heat through an organic Rankine cycle (ORC). The results show that the SOEC consumes (743.53 kW) less energy while producing more gH₂ (21.94 kg/h) compared to PEME (796.25 kW, 13.96 kg/h) and AE (797.69 kW, 10.74 kg/h). In addition, both the overall system and SOEC stack efficiencies are greater than those of PEME and AE, respectively. Although the investment cost required for AE (with and without H₂ compression consideration) is cheaper than SOEC and PEME in both scenarios, the cost of the H₂ produced by the SOEC is cheaper by more than 2 USD/kgH₂ compared to both other technologies.