The flame stability and heat transfer characteristics of methane-air mixtures in catalytic micro combustors were studied, using a two-dimensional computational fluid dynamics (CFD) model with detailed chemistry and transport. The effects of wall thermal conductivity, surface emissivity, fuel, flow velocity, and equivalence ratio were explored to provide guidelines for optimal design. Furthermore, the underlying mechanisms of heat and mass transfer for loss of flame stability were elucidated. Finally, stability diagrams were constructed and design recommendations were made. It was found that the heat loss strongly affects extinction, whereas the wall thermal conductivity greatly affects blowout. The presence of homogeneous chemistry extends blowout limits, especially for inlet velocities higher than 6 m/s. Increasing transverse heat transfer rate reduces stability, whereas increasing transverse mass transfer rate improves stability. Surface radiation behaves similarly to the heat conduction within the walls, but opposite trends are observed. High emissivity causes the flame to shift downstream. Methane exhibits much broader blowout limits. For a combustor with gap size of 0.8 mm, a residence time higher than 3 ms is required to prevent breakthrough, and inlet velocities lower than 0.8 m/s are the most desirable operation regime. Further increase of the wall thermal conductivity beyond 80 W/(m"K) could not yield an additional increase in stability. (C) 2016 Elsevier Ltd. All rights reserved.