Uncrewed aerial vehicles (UAVs) are increasingly becoming essential monitoring tools across a rapidly growing set of applications, due to their operational versatility,  relatively low operating cost, and provision of data at a range of spatial scales. However, UAV-based measurement methodologies and associated instruments for atmospheric research are still in their early stages and require extensive efforts to exploit their full potential. In Arctic regions, geological CH₄ seeps can  release CH₄ at rates significantly higher than typical biogenic sources and those associated with permafrost degradation processes; hence, accurate quantification of their emission rates is crucial for the overall CH₄ budget of the Arctic. The application of conventional greenhouse gas monitoring platforms – flux chambers and eddy-covariance towers – may become impractical as eddy-covariance towers are stationary point measuring devices that require long observation times with reliable footprint modeling to constrain emissions while flux chambers have a small footprints and therefore require multiple measurements and have a high potential of introducing disturbances. UAVs can overcome these limitations as they can capture the spatial extent of the gas plume released from a point source with minimal disturbance to the source. In July 2025, we deployed two UAV platforms with different sensing instruments to sample a known geological CH₄ seep located at the Mackenzie River Delta, Canada. We flew vertical "curtain" patterns with open-path and closed-path CH₄ instruments to sample gas concentrations in flux planes at different downwind distances from the gas seep. We first evaluated the performance of the UAV-mounted instrumentation, comparing the open- and closed-path greenhouse gas analyzers. We then compared two widely used quantification techniques – mass-balance and Gaussian plume inversion – finding that mass-balance approaches yielded the most robust quantification with smaller uncertainties. We estimate that the seep emission rate falls in the range of 7.1 to 16.2 kg CH₄ h^-1, with an average estimated rate of 11.4 ± 6.8 kg CH₄ h^-1. The emissions from this single point are equivalent to the biogenic flux from approximately 2.2 km² of the surrounding permafrost landscape, underscoring the need to assess the potentially significant contribution of geological seeps to regional and pan-Arctic carbon budgets.