Some results of experimental studies of the water-in-oil emulsions in RF and MW electromagnetic fields are presented. In an attempt to understand the phenomenon a mathematical model for a single emulsion droplet dynamics in radiofrequency (RF) and microwave (MW) electromagnetic fields is formulated. An algorithm for numerical solution of the problem is developed. The problem is solved accounting for the thermal motion induced by electromagnetic field in the fluid within the water droplet and in the surrounding liquid. The numerical solution revealed that the structures of arising convective flows induced by RF and MW electromagnetic fields are different. The results can help to understand the physical mechanisms of water-in-oil emulsion destruction in electromagnetic field.