Porous media combustion (PMC) is characterized by intense heat exchange from the combustion gases to the solid media, enabling higher temperatures at the outer surface of the solid matrix. This paper, for the first time, experimentally investigates how to control combustion inside a porous media matrix to take advantage of its hot outer surface for active emission to a thermophotovoltaic (TPV) system. This 'coupled porous media combustion-based thermophotovoltaic (PMC-TPV) system' requires a stable flame over (only) the narrow height where the photovoltaic cells are mounted. Thus, this study reports a systematic flame stability analysis for lean Air/methane mixtures to optimize the radiant performance of three different porous media combustor designs for thermophotovoltaic applications. In this study, the equivalence ratio was set at 0.7 and the firing rates were varied in order to find the stable and unstable regimes of each reactor. Results indicate that the use of a radiant reflector shifts the stable flame regimes and increases the radiant efficiency to 63% at an operating temperature of 1356 degrees C. Superadiabatic conditions were also found to be possible in this system, with a maximum temperature of 1538 degrees C, which improves the radiant emission spectrum for the photovoltaic (PV) cells. These fundamental combustion findings will help to define the operating parameters and improve the electrical conversion efficiency in future PMC-TPV systems.