Accurate Wheeler cap measurements, either in a narrow or a wide band, are critically affected by the postprocessing method employed to deduce efficiency values from raw data. Stringent cases like multiband or circularly polarized (CP) antennas cannot be handled accurately by typical postprocessing methods, but lend themselves to post-processing based on equivalent circuits. This paper revisits the equivalent-circuit Wheeler cap (EC-WCap) and modifies all steps of the algorithm, thus significantly enhancing its simplicity and speed, while maintaining a wideband measurement capacity. This enhancement of EC-WCap was driven by the need to accurately characterize multiband CP magneto-dielectric antennas built on externally biased ferrimagnetic compounds, which resist characterization by other Wheeler-cap-related post-processing methods.