The article discusses an innovative Power-to-Gas-to-Power (PtGtP) system designed to facilitate the transformation of surplus renewable electricity into methane, serving as a versatile energy carrier. This system integrates an electrolyzer, a methanation unit, an Allam cycle, and a waste heat recovery unit, aimed at achieving a zero-emission energy storage solution. The study highlights the significance of PtG technologies in enabling sustainable energy systems and emphasizes the unique grid stabilization and energy storage capabilities offered by PtGtP systems. The research delves into uncertainty and global sensitivity analysis for eight key parameters, pinpointing the combustion chamber and methanation reactor temperatures as critical factors influencing system performance. A multi-objective optimization (MOO) strategy is employed to strike a balance between maximizing system efficiency and minimizing costs. The resulting Pareto frontier showcases a variety of optimal solutions, boasting exergy round trip-efficiencies ranging from 27.9% to 33.3% at corresponding cost rates varying between 0.88 to 0.98 $/second. Furthermore, the article employs the TOPSIS decision-making criteria to identify a well-rounded compromise solution that achieves a notable 33.1% exergy round-trip efficiency with a cost rate of 0.89 $/second. This optimal compromise solution underscores the feasibility and effectiveness of the PtGtP system in efficiently storing and utilizing renewable energy. Overall, the study underscores the importance of innovative energy conversion and storage methods, particularly in the context of the global transition towards sustainable energy systems.