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The catalytic combustion of methane/air mixtures is investigated experimentally and numerically at gas turbine relevant conditions (inlet temperatures up to 873 K, pressures up to 15 bar and spatial velocities up to 3 × 10 6 h −1 ). Experiments are performed in a sub-scale test rig, consisting of a metallic honeycomb structure with alternately coated (Pd-based catalyst) channels. Simulations are carried out with a two-dimensional elliptic fluid mechanical code that incorporates detailed transport and heat loss mechanisms, and realistic heterogeneous and homogeneous chemistry description. The methodology for extracting heterogeneous kinetic data from the experiments is presented, and the effects of catalytic activity and channel geometry (length and hydraulic diameter) on reactor performance are elucidated. A global catalytic kinetic step provides excellent agreement (at temperatures below 950 K) between the measured and predicted fuel conversion, over a wide range of parameter variation (channel hydraulic diameter and length, pressure, and inlet temperature). It is shown that, under a certain combination of catalytic activity and channel length, the absolute temperature rise across the catalyst becomes essentially independent of pressure, a feature highly desirable for many practical systems. Even though the computed catalyst surface temperatures remain well below the decomposition temperature of PdO, a significant section of the catalyst-amounting up to 30% of the total reactor length-contributes minimally to the total fuel conversion, suggesting catalytic activity design improvements in the reactor entry.