Power-to-methane technology has been considered as a promising alternative to cope with seasonal storage of renewable energy and the utilization of CO2 captured from various sources, due to the existing infrastructure for massive methane storage and distribution. The performance of a power-to-methane system is almost defined by the type and the design point of the electrolyzer. The inherent high electrical efficiency of solid oxide electrolyzer makes it rather promising for a highly efficient power-to-methane system. However, the large amount of heat needed for steam generation limits the overall efficiency of a standalone electrolyzer. Fortunately, the strong exothermic methanation reaction offers a good opportunity for heat integration, thus possibly increasing the overall HHV efficiency above 85 %. Regarding to this context, a power-to-methane test rig based on a full stack of solid oxide electrolyzer is currently under design and demonstration. In this paper, the critical issues related to the design of such an integrated system are addressed: (1) selecting the nominal operating point of the electrolyzer to minimize electrical heating at no cost of efficiency and (2) maximizing the benefit from the system integration at no cost of operation flexibility. A quasi 2D model of the electrolyzer considering detailed mass transport across the electrodes has been developed and calibrated to understand the electrolyzer performance that is not revealed by experiments. Then, the system design is investigated by varying the utilization factor and the cell temperature. The most promising practical design point with an overall efficiency around 85 % and no electrical heating is selected with the design of a specific heat exchanger network to maximize the heat integration with a minimum number of connections between the electrolyzer and the methanation subsystems.