The hetero-/homogeneous combustion of CH4/O2/N2 mixtures over rhodium was investigated experimentally and numerically at fuel-lean equivalence ratios φ = 0.30–0.40, pressures 2–12 bar, and catalyst temperatures 700–1250 K. Experiments were performed in an optically accessible channel-flow reactor coated with rhodium and included in situ Raman measurements of major gas-phase species concentrations across the channel boundary layer for evaluating the catalytic processes, and planar laser induced fluorescence (LIF) of the OH radical for assessing homogeneous combustion. Computations were carried out with a 2-D elliptic code, using detailed heterogeneous and homogeneous chemical reaction mechanisms. Comparisons between Raman-measured and numerically-predicted transverse profiles of the limiting reactant (methane) mole fractions have led to the evaluation of the performance of detailed surface reaction mechanisms and to the construction of a one-step catalytic reaction suitable for pressures up to 12 bar. For the investigated range 2–12 bar, the catalytic reactivity of methane over rhodium exhibited an overall positive pressure dependence ∼p^0.30, which was weaker compared to an earlier-reported pressure dependence of methane over platinum (∼p^0.47). Comparisons of the planar OH-LIF measurements with numerical simulations employing different gas-phase reaction mechanisms demonstrated that the correct prediction of homogeneous ignition was particularly demanding at the present low equivalence ratios and moderate reactor temperatures. An elementary gaseous reaction mechanism was shown to reproduce the measured homogeneous ignition distances at all pressures, particularly when used in conjunction with the herein proposed one-step catalytic reaction.