Atmospheric methane (CH4) varied with climate during the Quaternary, rising from a concentration of 375 p.p.b.v. during the last glacial maximum (LGM) 21,000 years ago, to 680 p.p.b.v. at the beginning of the industrial revolution. However, the causes of this increase remain unclear; proposed hypotheses rely on fluctuations in either the magnitude of CH4 sources or CH4 atmospheric lifetime, or both. Here we use an Earth System model to provide a comprehensive assessment of these competing hypotheses, including estimates of uncertainty. We show that in this model, the global LGM CH4 source was reduced by 28-46%, and the lifetime increased by 2-8%, with a best-estimate LGM CH4 concentration of 463-480 p.p.b.v. Simulating the observed LGM concentration requires a 46-49% reduction in sources, indicating that we cannot reconcile the observed amplitude. This highlights the need for better understanding of the effects of low CO2 and cooler climate on wetlands and other natural CH4 sources.