The production of methanol by use of water electrolysis and hydrogenation of carbon dioxide (Power-to-Methanol) is a promising pathway to reduce greenhouse gas emissions. The concept of process intensification and the associated utilization of an in-situ coupling of methanol synthesis with proton-conducting Solid Oxide Electrolysis Cells (H+-SOEC) is a possible way to increase the energy efficiency of this process. Based on an extensive literature research, a novel Power-to-Methanol reactor concept for a concentric in-situ-integration of a tubular H+-SOEC has been designed, manufactured and operated at the Chair of Hydrogen and Nuclear Energy at the Technische Universität Dresden. The conducted experiments served as reference points for the process simulations performed in the second part of this thesis. Here, the Power-to-Methanol process has been modelled and simulated by means of process systems engineering methods to evaluate the in-situ-process in comparison to an conventional uncoupled set-up based on planar H+-SOECs. For this task, a novel and firm H+-SOEC process model was developed and implemented. In addition, the heat integration potential and profitability of the two Power-to-Methanol concepts have been investigated by Pinch Point and Techno-Economic Analysis. On the experimental side, a proof-of-concept of the novel reactor design was demonstrated, but limitations regarding the optimal thermal profile and operational flexibility of each process were identified. Furthermore, the methanol production rate showed potential for further improvement. The simulation results have helped to understand the process characteristics and to locate optimal operation points regarding current density, temperature and pressure. In an optimised operation scenario, high energy efficiencies for both tubular in-situ and planar set-ups have been achieved, by means of harnessing the heat integration potential through exothermic H+-SOEC operation. Notwithstanding the above, planar set-ups have demonstrated to be substantially more profitable than tubular systems. This has been the first investigation on Power-to-Methanol processes based on H+-SOEC. The present work helps to identify remaining development objectives for the use of H+-SOEC and Power-to-Methanol processes in general. The results from experiments and simulations indicate the challenging utilization of tubular electrolysis cells, but also revealed new research priorities that should be addressed in the future.