To establish robust calibration and measurement capabilities (CMCs) for atmospheric methane (CH4) stable isotope ratios, National Metrology Institutes (NMIs) and Designated Institutes (DIs) need a comprehensive understanding of the underlying measurement techniques, reference materials (RMs), calibration hierarchies, value assignment, uncertainty evaluation, and inter-laboratory comparison activities. This review, developed by the CH4 Task Team within the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology (CCQM) Gas Analysis Working Group (GAWG) and the Isotope Ratio Working Group (IRWG), provides key insights for developing these capabilities at NMIs/DIs. The World Meteorological Organization (WMO) recommended network compatibility goals for atmospheric methane stable isotope ratio monitoring, expressed as isotope delta values, are 0.02‰ for the stable carbon isotope delta (δ13C) value and 1‰ for the stable hydrogen isotope delta (δ2H) value, with extended targets of 0.2‰ for δ13C and 5‰ for δ2H. Global inter-laboratory comparisons have revealed offsets of up to 0.5‰ for δ13C and 13‰ for δ2H measurements, substantially exceeding the WMO targets. To address these discrepancies, steady progress is being made, particularly by expert isotope laboratories, with increasing engagement from NMIs/DIs. Improved measurement techniques and the use of common RMs are bringing measurements closer to the WMO goals. This overview not only reviews the components necessary for establishing NMI/DI CMCs but also provides actionable recommendations to further align global measurements, including the development of standardized protocols, adoption of the VPDB carbon isotope delta scale for atmospheric data harmonization, and international comparison studies to support NMI/DIs in their CMC claims. These actions are critical for achieving long-term consistency and advancing global standards for atmospheric methane stable isotope ratio measurements.