Green hydrogen technologies are crucial for decarbonization purposes, while cogeneration offers efficient heat and power generation. Integrating green hydrogen and cogeneration brings numerous benefits, optimizing energy utilization, reducing emissions, and supporting the transition to a sustainable future. While there are numerous studies examining the integration of combined heat and power with Power to Gas, certain aspects still requires a more detailed analysis, especially for internal combustion engines fuelled by natural gas, due to their widespread adoption as one of the primary technologies in use. Therefore, this paper presents a comprehensive numerical 0-D dynamic simulation model, implemented within the TRNSYS environment, considering internal combustion engines fuelled by natural gas. Specifically, the study focuses on capturing CO2 from exhaust gases and producing green hydrogen from electrolysis. Based on these considerations, two configurations are proposed: the first involves the methanation reaction, while the second entails the production of a hydromethane mixture. The aim is to evaluate the technical and economic feasibility of these configurations and compare their performance within the Power to Gas framework. Self-sufficiency from the national electricity grid has been almost achieved for the two configurations, considering an industrial case. The production of hydromethane allows smaller photovoltaic plant (81 kWp) compared to the production of synthetic methane (670 kWp) where a high quantity of hydrogen is required, especially if all the carbon dioxide captured is used in the methanation process. Encouraging economic results with payback times below ten years have been obtained with the use of hydromethane. Moreover, hydromethane shows potential residential applications, with small required photovoltaic sizes.