Environmental concerns surrounding the use of high-sulfur fuel oil (HFO), a marine fuel derived from refinery vacuum residue, motivate the exploration of alternative solutions. Burning high-sulfur fuel oil (HFO) is a major source of air pollution, acid rain, ocean acidification, and climate change. When HFO is burned, it releases sulfur dioxide (SO2) into the air, a harmful gas that can cause respiratory problems, heart disease, and cancer. SO2 emissions can also contribute to acid rain, which can damage forests and lakes. Several countries and international organizations have taken steps to reduce HFO emissions from ships. For example, the International Maritime Organization (IMO) has implemented a global sulfur cap for marine fuels, which limits the sulfur content of fuel to 0.5% by mass. In addition, there is a worldwide effort to encourage the use of low-carbon gases to help reduce greenhouse gas (GHG) emissions. There are several alternative fuels that can be used in ships instead of HFO, such as liquefied natural gas (LNG), methanol, and hydrogen. These fuels are cleaner and more environmentally friendly than HFO. The aim of this study is to develop a process integration framework to co-produce methanol and hydrogen from vacuum residue while minimizing the sulfur and carbon emissions. Two process models have been developed in this study to produce methanol and hydrogen from vacuum residue. In case 1, vacuum residue is gasified using oxygen—steam and the syngas leaving the gasifier is processed to produce both methanol and hydrogen. Case 2 shares the same process model as case 1 except it is concentrated on mainly methanol production from vacuum residue. Both models are techno-economically compared in terms of methanol and H2 production rates, specific energy requirements, carbon conversion, CO2 specific emissions, overall process efficiencies, and project feasibility while considering the fluctuation of vacuum residue feed price from 0.022 $/kg to 0.11 $/kg. The comparative analysis showed that case 2 offers an 86.01% lower specific energy requirement (GJ) for each kilogram (kg) of fuel produced. The CO2 specific emission also decreased in case 2 by 69.76% compared to case 1. In addition, the calculated total net fuel production cost is 0.453 $/kg and 0.223 $/kg at 0.066 $/kg for case 1 and 2, respectively. Overall, case 2 exhibits better project feasibility compared to case 1 with higher process performance and lower production costs.