The observed rise in atmospheric methane (CH
4
) from 375 ppbv during the Last Glacial Maximum (LGM: 21,000 years ago) to 680 ppbv during the late preindustrial era is not well understood. Atmospheric chemistry considerations implicate an increase in CH
4
sources, but process‐based estimates fail to reproduce the required amplitude. CH
4
stable isotopes provide complementary information that can help constrain the underlying causes of the increase. We combine Earth System model simulations of the late preindustrial and LGM CH
4
cycles, including process‐based estimates of the isotopic discrimination of vegetation, in a box model of atmospheric CH
4
and its isotopes. Using a Bayesian approach, we show how model‐based constraints and ice core observations may be combined in a consistent probabilistic framework. The resultant posterior distributions point to a strong reduction in wetland and other biogenic CH
4
emissions during the LGM, with a modest increase in the geological source, or potentially natural or anthropogenic fires, accounting for the observed enrichment of
δ
13
CH
4
.