The transition towards clean renewable energy sources, where wind and solar are prone to variation, requires adequate energy storage. Power-to-methane (PtM) systems can be part of the solution. Specifically, solid-oxide-electrolyser (SOE) based PtM systems benefit from higher efficiency because (1) steam electrolysis requires less electrical energy than liquid water electrolysis, and (2) the heat generated by the methanation reaction can be harvested to generate the steam fed to the SOE. There have been few attempts at coupling an SOE to a catalytic methanation reactor but none were fully successful while evaporating directly in the reactor's cooling system. A fixed-bed methanation reactor of a practically relevant scale (5-10 kW gas input), cooled directly using partially evaporated water, was designed, built, operated, and simulated. CO2 methanation and syngas methanation were both tested and the measured hot spot was maintained under 700°C, but the outlet gas quality was under the level required for direct injection into the Swiss natural gas grid. Nevertheless, results indicate that increasing both the reaction pressure and the cooling water pressure could improve the gas quality. In CO2 methanation, the stability of the steam production was comparable to a commercial evaporator designed to supply an SOE. In syngas methanation, the need to inject steam with the reactant, to limit the risk of carbon formation over the entire operating range, can nullify the gain in steam production from the more exothermal CO methanation. Multiple practical insights were gained in operating the reactor, for future developments. On a system level, multi-objective optimizations were performed on a SOE-based PtM system where heat was recovered only through the heat cascade to assess the effects of the reactor's key design parameters and the response on the system performance: I. Including heat loss and H2 conversion measured in the reactor, and limiting the evaporation process to the reactor's cooling system, can force a higher SOE stack utilization factor to avoid or to lower the dependency on an external evaporator - though the SOE performance worsens. II. The water at the outlet of the electrolyser in steam and CO2 co-electrolysis, if not condensed, can satisfy the steam required at the reactor's inlet, allowing a lower utilization factor. III. Pressurized evaporation inside the reactor's cooling system provides the possibility of capturing available heat from higher temperature streams to superheat the steam which can then drive a turbine to produce electricity further improving the system's performance. This method allows the extraction of heat from the electrolyser's outlet flows if operated exothermally. Lastly, a methanation unit with ideal heat exchangers was optimized to identify thermodynamic trade-offs. The higher-heating value efficiency and co-generation efficiency were found to be competing, as the latter attempts to maximize steam production though it can negatively impact the heat recovery. The results of these studies provide guidance into the continued development of a SOE-based PtM system and its operation.