The key area of the Arctic Ocean for atmospheric venting of CH4 is the East Siberian Arctic Shelf (ESAS). Leakage of methane through shallow ESAS waters needs to be considered in interactions between the biogeosphere and a warming Arctic climate. The development of remote sensing techniques for gas seepage detection and mapping is crucially needed for further applications in the ESAS and other areas of interest. Given the extent of the seepage areas and the magnitude of current and potential future emissions, new approaches are required to effectively, rapidly, and quantitatively survey the large seepage areas. Here, we consider the main features of gas seep detection on the sea surface in the characteristics of wind waves and radar signals. The kinematics of wave packets based on the kinetic equation for the spectral density of the wave action of surface waves is described. The results of a full-scale experiment on the remote radar observation of a model gas seep to the sea surface in the radar equipment signals are considered. The characteristic radar signatures of the gas seep in a wide range of hydrometeorological conditions, the parameters of which were recorded synchronously with the radar mapping, were determined. The results of the first radar observations of natural methane seeps on the ESAS are presented, and their radar contrasts are evaluated. The theoretical conclusions are in good qualitative agreement with the results of the model experiment and field studies and can be used for further research in aquatic areas with potential gas seepage, both of natural or anthropogenic origin, such as bubbling release from broken underwater gas pipelines.