We present a new machine-learning approach for interpolation of frequency response functions, e.g. for electric circuits, based on a rational kernel-based interpolation method. The suggested method combines Szegö kernel interpolation with a suitable pseudo-kernel and a few rational basis functions inspired from vector fitting as well as a dedicated tuning and model selection procedure. We show that the method yields comparable accuracy as the established state-of-the-art methods adaptive Antoulas-Anderson and vector fitting for the considered benchmarks.