This paper is devoted to the prediction of self-ignition and quenching limits in a catalytic micro-burner in the context of a zero-dimensional approach that was originally developed by Semenov and Zel'dovich for the analysis of self-accelerating chemical reactions and critical phenomena in an ideal homogeneous chemical reactor. We formulated the analytical criteria for self-ignition and quenching in the catalytic micro-burner, and the sensitivity equations that show the effect of the variations of geometrical, chemical and regime parameters on the boundary of the operating regimes. We compare the theoretical self-ignition and quenching limits with those known in the literature for the CH4-air and CH4/H-2-air mixtures obtained on the micro-structured burner with a Pt-LaMnO3 catalytic honeycomb. Agreement was found between the theoretical and experimental results. Our semi-empirical analysis explains qualitatively the different effects of hydrogen addition to a methane-air mixture on self-ignition and the quenching limits that were observed in the analyzed experiments, and predicts these limits for the operation regimes that were not tested in the experiments. We perform the sensitivity analysis of the self-ignition problem, which shows how small variations in the geometrical, chemical and thermodynamic parameters influence the minimal ignition temperature in the analyzed experiments with the CH4-air and CH4/H-2-air mixtures, and propose a way to perform sensitivity analysis for the quenching problem. (C) 2015 Elsevier Ltd. All rights reserved.