The power-to-methane process using a solid-oxide electrolyser, followed by an exothermic methanation reactor, is effective for the production of an energy carrier (synthesis methane) that can be readily stored and transported at a large scale. A significant gain of the coupling is the steam generation from the heat produced by the methanation reaction for the more effective steam electrolysis (compared to liquid water electrolysis). This paper investigates, both theoretically and experimentally, the system integrability and operability of an evaporating water-cooled methanation reactor designed for thermal coupling with a solid-oxide electrolyser. The results show that the pressurized steam generation directly by the reactor's cooling system improves the flexibility of the system design. Under certain conditions, an increase in overall power-to-methane efficiency of more than 3 % can be obtained from the use of a superheater and a turbine located after the evaporation process. The parametric study of the methanation reactor indicates that decreasing the flowrate of the H2 and CO2 mixture, increasing the reaction gas pressure and increasing the cooling system pressure (saturation temperature) shifts the hot spot towards the inlet and improves the H2 conversion rate, which can reach above 97 %. It was determined that, under steady-state operation, the steam generation can be sufficiently stable for injection into the solid-oxide electrolyser; rapid pulsations with a standard deviation under 10% were measured. The calibrated 1D pseudo-homogeneous plug flow reactor model captures many of the trends, though, the assessment is limited without the exact kinetic model of the catalyst pellets.