The heterogeneous and homogeneous combustion of fuel-lean CH4/O2/N2 mixtures over PdO was investigated experimentally and numerically at equivalence ratios φ = 0.27–0.44, pressures 1–12 bar and surface temperatures 710–1075 K. In situ Raman measurements of major gas-phase species concentrations across the boundary layer of a channel-flow catalytic reactor assessed the heterogeneous reactivity, while planar laser induced fluorescence (LIF) of the OH radical monitored homogeneous combustion. Simulations were performed using a 2-D code with detailed heterogeneous and homogeneous reaction mechanisms. Comparisons between Raman-measured and predicted transverse profiles of major species mole fractions attested the atmospheric-pressure suitability of a detailed surface mechanism and allowed for the construction of a global catalytic step valid in the range 1–12 bar. The methane catalytic reaction rate exhibited an overall pressure dependence ∼p^(1−n) where the exponent n was itself a monotonically increasing function of pressure, rising from 0.58 at 3 bar to 1.02 at 12 bar. This resulted in a non-monotonic pressure dependence of the catalytic reaction rate in the range 1–12 bar, a behavior in stark contrast to other noble metals (Pt and Rh) where the methane reaction rates always increased with rising pressure. Surface temperatures remained well-below the PdO decomposition temperature at each corresponding pressure, owning largely to the “self-regulating” temperature effect of PdO, and this in turn mitigated homogeneous ignition. Simulations using the PdO decomposition temperatures as boundary conditions for the wall temperatures were further performed for practical CH4/air catalytic reactors in power generation systems. It was shown that for p < 7 bar (a range relevant to microreactors) homogeneous ignition was altogether suppressed. For higher pressures relevant to gas-turbine burners, however, gaseous combustion ought to be considered in the reactor design.