Understanding and controlling the combustion of clean and efficient fuel blends, like methane + hydrogen, is essential for optimizing energy production processes and minimizing environmental impacts. To extend the available experimental database on CH₄ + H₂ flame speciation, this paper reports novel measurement data on the chemical structure of laminar premixed burner-stabilized CH₄/H₂/O₂/Ar flames. The experiments cover various equivalence ratios (φ = 0.8 and φ = 1.2), hydrogen content amounts in the CH₄/H₂ blend (X_H2 = 25%, 50% and 75%), and different pressures (1, 3 and 5 atm). The flame-sampling molecular-beam mass spectrometry (MBMS) technique was used to detect reactants, major products, and several combustion intermediates, including major flame radicals. Starting with the detailed model AramcoMech 2.0, two reduced kinetic mechanisms with different levels of detail for the combustion of CH₄/H₂ blends are reported: RMech1 (30 species and 70 reactions) and RMech2 (21 species and 31 reactions). Validated against the literature data for laminar burning velocity and ignition delays, these mechanisms were demonstrated to reasonably predict the effect of pressure and hydrogen content in the mixture on the peak mole fractions of intermediates and adequately describe the new data for the structure of fuel-lean flames, which are relevant to gas turbine conditions.