Frequency Response Analysis compares measured transfer functions of power transformers. Deviations of frequency response curves indicate electrical or mechanical damages of windings. As assessments are done by experts, no objective guidelines for interpretation of measurement results exist. This paper deals with approximation of measured power transformer frequency responses using complex rational function models. A fitting algorithm maps the information contained in measured curves on a pole-zero model of reduced complexity. The aim is to develop an algorithm for automated interpretation using analytical models created on the basis of measurement data. Requirements of accuracy of the approximation models for purposes of Frequency Response Analysis are considered. An enhanced algorithm for complex rational function estimation based on the proven Vector Fitting method is presented. Finally, application of the algorithm with real measured data is demonstrated.