Methane (CH₄) is a powerful greenhouse gas and plays a key part in global atmospheric chemistry. Natural geological emissions (fossil methane vented naturally from marine and terrestrial seeps and mud volcanoes) are thought to contribute around 52 teragrams of methane per year to the global methane source, about 10 per cent of the total, but both bottom-up methods (measuring emissions) and top-down approaches (measuring atmospheric mole fractions and isotopes) for constraining these geological emissions have been associated with large uncertainties. Here we use ice core measurements to quantify the absolute amount of radiocarbon-containing methane (¹⁴CH₄) in the past atmosphere and show that geological methane emissions were no higher than 15.4 teragrams per year (95 per cent confidence), averaged over the abrupt warming event that occurred between the Younger Dryas and Preboreal intervals, approximately 11,600 years ago. Assuming that past geological methane emissions were no lower than today, our results indicate that current estimates of today's natural geological methane emissions (about 52 teragrams per year) are too high and, by extension, that current estimates of anthropogenic fossil methane emissions are too low. Our results also improve on and confirm earlier findings that the rapid increase of about 50 per cent in mole fraction of atmospheric methane at the Younger Dryas-Preboreal event was driven by contemporaneous methane from sources such as wetlands; our findings constrain the contribution from old carbon reservoirs (marine methane hydrates, permafrost and methane trapped under ice) to 19 per cent or less (95 per cent confidence). To the extent that the characteristics of the most recent deglaciation and the Younger Dryas-Preboreal warming are comparable to those of the current anthropogenic warming, our measurements suggest that large future atmospheric releases of methane from old carbon sources are unlikely to occur.