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We use a hybrid model including asymptotic expressions of the spheroidal wave functions (SWFs) to obtain a reliable broadband solution for the electromagnetic induction (EMI) response from a conducting and permeable spheroid. We obtain this broadband response, valid in the magnetoquasistatic regime from zero to hundreds of kilohertz, by combining three different techniques, each applicable over a different frequency range. At low frequencies, the exact analytical solution is used. At midrange frequencies, asymptotic expressions for the angular and radial SWFs are incorporated into the exact solution in order to maintain a stable solution for the induced magnetic field. At higher frequencies, a small penetration approximation (SPA) solution is used when the SPA solution approaches the asymptotically assisted solution to within some predefined tolerance. Validation of this combined technique is accomplished through the comparison of the induced magnetic field predicted by our model to both a finite element/boundary integral (FE-BI) numerical solution and experimental data from various spheroids taken by an ultrawideband EMI instrument.