The hetero-/homogeneous combustion of fuel-rich H2/O2/N2 mixtures (equivalence ratios φ = 2.5-6.5) was investigated experimentally and numerically in a platinum-coated channel at pressures p = 1-14 bar. One-dimensional Raman measurements of major gas-phase species concentrations over the catalyst boundary layer assessed the heterogeneous combustion processes, while planar laser induced fluorescence (LIF) of OH at pressures below ∼5 bar and of hot-O2 at pressures above ∼5 bar (wherein OH-LIF was not applicable) determined the onset of homogeneous ignition. Simulations were carried out using a 2-D code with detailed hetero-/homogeneous chemical reaction schemes and transport. Both Raman measurements and numerical simulations attested a transport-limited catalytic conversion of the deficient O2 reactant over the gas-phase induction zones. The agreement between measured and predicted homogeneous ignition distances was better than 12%, thus establishing the aptness of the employed hetero/homogeneous chemical reaction mechanisms. Analytical homogeneous ignition criteria revealed that the catalytic reaction pathway introduced a scaling factor 1/p to the homogeneous ignition distances. This outcome, in conjunction with the intricate pressure dependence of the gaseous ignition chemistry of hydrogen, yielded shorter homogeneous ignition distances at 14 bar compared to 1 bar. The practical implication for gas turbine burners utilizing the catalytic-rich/gaseous-lean combustion concept was that the high operating pressures of such systems promoted the onset of homogeneous ignition within the catalytic module. Sensitivity analysis has finally identified the key catalytic and gaseous reactions affecting homogeneous ignition.