The catalytic synthesis of methane from H₂ and CO₂, which is an efficient way for the production of synthetic natural gas (SNG) by utilizing the H₂ originating from carbon-free renewable power sources and the greenhouse gas CO₂, was investigated in a non-isothermal channel-flow reactor coated with Ni/Al₂O₃ at pressures 1.5–10 bar, H₂:CO₂ volumetric ratios 4–6, and surface temperatures 450–760 K. In situ, spatially resolved Raman measurements of gas-phase species concentrations across the channel height were complemented by gas chromatography analysis of the exhaust gas. Two-dimensional simulations were carried out, using elementary catalytic and gaseous chemical reaction mechanisms and detailed transport. Comparisons of the Raman data and simulations revealed that the preferential diffusion of H₂ drastically altered the local H₂:CO₂ ratios at the catalytic walls, which attained values up to 8 times higher than the corresponding inlet values. This behavior exemplified the caution needed when performing kinetic studies in the mixed kinetically/transport controlled regime. The production of methane increased with increasing pressure and decreasing H₂:CO₂ ratio. At the highest ratio H₂:CO₂ = 6, the simulations underpredicted (overpredicted) the measured reactant (product) mole fractions, however, as H₂:CO₂ decreased, the trend was reversed. The discrepancies reduced with increasing pressure, resulting in a model overprediction of methane by 7.4% at 10 bar. Methane was produced from C(s) via successive hydrogenation. C(s) was in turn produced from COOH(s), followed by dissociation of COOH(s) to CO(s), and finally H-assisted dissociation of CO(s) to C(s). Gas-phase chemistry was negligible over the investigated conditions. The in-channel Raman measurements in conjunction with the exhaust gas analysis facilitated the construction of a global step for the studied reaction. The methane synthesis was assessed to follow a ∼p^0.41 pressure dependence over the temperature range 520–680 K.