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The secondary field produced by 3-D highly permeable and conductive objects is computed in the electromagnetic induction regime, with the purpose of modeling unexploded ordnances (UXOs) and surrounding clutter. The analytical formulation is based on the ellipsoidal coordinate system that is able to model real 3-D geometries as opposed to bodies of revolutions like within a spheroidal approach. At the frequencies of interest (tens of hertz to hundreds of kilohertz), conduction currents in the soil are negligible, and the fields are computed in the magnetoquasistatic regime based on the Laplace equation. Inside the objects, where the wave equation governs the field distribution, the currents are assumed to have a small penetration depth, allowing for the analytical simplification of the field components, which become decoupled at the surface. This approximation, which is valid across the entire frequency spectrum because of the high permeability and conductivity, avoids the necessity of using ellipsoidal wave functions and results in a considerable saving of computational time. Numerical results favorably compare with numerical and experimental data, which proves the usefulness of our method to model UXOs in clutter-contaminated soils. Finally, the optimization approach used to match our numerical predictions with experimental data demonstrates the possibility of remotely inferring the material properties of objects.