Catalytic combustion of methane mixed with hydrogen in micro-scale channels is becoming a key research topic, for various portable power generation devices that could replace current batteries to meet the increasing demand for more efficient, longer lasting and more environmentally friendly energy-consuming utilizations. The present work deals with the investigation on the performance of catalyst 2% Pd over 5% LaMnO3·ZrO2 (PLZ), lined on silicon carbide (SC) or cordierite (CD) monoliths, for the CH4/H2/air lean mixtures oxidation. The bare and coated monoliths were tested into a lab-microreactor designed to provide a favourable environment for microscale combustion of various CH4/H2/air lean mixtures to reach high power density (7.6 MWth m−3; GHSV 16,000 h−1). The main goal of the catalytic combustion tests was to select the best settings to achieve stable combustion conditions at the lowest possible temperature, i.e., full CH4 conversion with the minimum H2 concentration in the reactive mixture, accompanied by the lowest possible CO concentration.Depending on the thermal conductivity of the tested monoliths, the existence of the steady-state multiplicity was verified, mainly when the H2 concentration was quite low. Basically, CD monoliths exhibited shorter ignition times compared to SC ones, due to the formation of spatially localized hot spots that promoted catalytic ignition. At the same time, the CD monoliths required shorter times to reach steady-state. But SC materials assured longer time on stream operations. The presence of the catalyst lined on both monoliths allowed reaching lower CO emissions. The best results belonged to the coated SiC monolith, with very low H2 concentration in the mixtures.