Micro-scale combustion is an attractive alternative as a power source for numerous applications. The high-energy densities of hydrocarbon fuels make micro-scale combustors particularly appealing in comparison to fuel cells, batteries and other power generation devices. One of the major difficulties in the development of a micro-scale reactor is to sustain stable combustion in a small device with a high surface-to-volume ratio. To this end, catalytic combustion is considered a viable means to extend the operating range of combustors. In this work, a new stagnation-point flow burner facility has been developed to provide a canonical framework to study the interactions between fluid dynamics and chemical reactions in the gas-phase and heterogeneous modes. The stagnation-point flow burner is used to study extinction limits of catalyst-assisted premixed methane combustion. Basic characterization of the burner is performed and preliminary experimental data for extinction limits are presented as a function of the flow strain rate, mixture equivalence ratio, and the level of catalytic activity.