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This paper describes the design of sinuous antenna reflector feeds using blended rational interpolation. The blended rational interpolation method is developed to interpolate a sparse set of high-fidelity (HF) data while following the trends of a denser set of low-fidelity (LF) data. The HF data are obtained by full-wave computational electromagnetics simulations of the input impedance of a pyramidal sinuous antenna above a ground plane, while the LF data are obtained, at a significantly reduced computational cost, through simulations of a truncated version of the same antenna. Comparisons with other interpolation schemes, both for HF as well as for multifidelity data sets, are presented. It is shown that the blended rational interpolation scheme presented herein yields improved accuracy in most cases. A design example is also presented where a global model of the maximum input reflection coefficient over frequency is built over the design space and thus used to identify the region of acceptable performance.Comparisons with a validation set of HF data resulted in similar results, with the blended rational interpolation model requiring significantly shorter computer simulation time. KEYWORDSbroadband antenna, multifidelity modelling, radio astronomy antennas, rational interpolation, reflector feed, sinuous antenna Int J Numer Model. 2019;32:e2458.wileyonlinelibrary.com/journal/jnm