An initial study of a novel method to diagnose the effects of the various degradation mechanisms on the power transformers, while in operation, is presented. We model a transformer winding surrounded by the transformer-tank wall and the magnetic core as a two-dimensional parallel plate waveguide, where one plate represents the wall of the transformer tank and the other plate represents the iron core that conducts the magnetic flux. In between there is a set of parallel conductors representing the winding segments. The new principle is to insert antennas inside the transformer tank to radiate and measure microwave fields that interact with the metallic structure and the insulation. The responses from the radiated waves are assumed to be sensitive to material properties that reflect any harmful deterioration processes. In particular, we study the mechanical deformations of the transformer winding by determining the locations of the individual conductors, from measurements of the scattered fields at both ends. The propagation problem is solved accurately and efficiently by conventional waveguide theory, including mode- matching and cascading techniques. We employ optimization as a suitable method to solve the inverse problem and obtain a good agreement between the calculated and measured positions of winding segments.