Ice core records from Greenland and Antarctica reveal large and rapid variations in atmospheric methane concentrations ([CH₄]) in response to abrupt climate change. Two such events occurred at the Oldest Dryas (OD) - Bølling and Younger Dryas (YD) - Preboreal (PB) climatic transitions during the last glacial termination. A record of ¹⁴C of atmospheric CH₄ (¹⁴CH₄) through these transitions can help to identify the sources of the [CH4] increases and constrain the fossil fraction of paleo CH₄ budgets. Very large (1̃00 L STP) samples of paleoatmospheric air are needed for such ¹⁴CH₄ measurements. To obtain these samples, ancient ice outcropping at an ice-margin ablation site in West Greenland was explored. Ice sections dating to the last glacial termination were identified and found to contain high-quality gas records. A new method for large-scale air extraction from glacial ice was developed and twelve large air samples from the YD-PB and the OD-Bølling transitions were obtained. New methods were also developed for processing this air for ¹⁴CH₄. ¹⁴CH₄ procedural blanks were greatly reduced through the construction of a new CH₄ conversion line utilizing platinized quartz wool for CH₄ combustion and the use of an ultra high purity iron catalyst for graphitization. The overall ¹⁴CH₄ processing blank was 0.75 ± 0.38 pMC. Measured ¹⁴CH₄ values were too high by 14 - 38% as compared to the highest expected values based on paleoatmospheric ¹⁴CO₂. In-situ production of CH₄ and direct cosmogenic production of ¹⁴CH₄ molecules in ablating ice were identified as the two most likely mechanisms that elevated ¹⁴CH₄ . Sample ¹⁴CH₄ was then corrected for both mechanisms, however these corrections are speculative and do not allow any definite conclusions to be drawn from the results. Corrected ¹⁴CH₄ results suggest that there was a 7% increase in the fossil CH₄ fraction from the YD to the PB. The corrected ¹⁴CH₄ results also suggest no large changes in the fossil fraction between the OD and the YD. Finally, the corrected results suggest that up to 80% of the OD - Bølling [CH₄]- rise (1̃00 ppb) was due to ¹⁴C -free CH₄