We construct a spheroidal-mode approach for unexploded ordnance (UXO) inversion under time harmonic excitations in the magneto-quasistatic regime. Use of spheroidal modes gives us the ability to deal with a variety of objects from elongated needles to flat plates, with better accuracy than the simple dipole models commonly used. The method can also be used for complex objects whose shape cannot be well approximated by spheroidal surfaces. In this case, we define a spheroidal surface surrounding the objects as a computational device for obtaining the object's scattered field in the spheroidal coordinate system. The coefficients obtained in the spheroidal coordinate system are shown to be the characteristics of the object. Stored in a library, they can produce fast and complete forward models for use in pattern matching inversion. For a single spheroidal object reconstruction, a differential evolution optimization algorithm, combined with the spheroidal mode formulation, inverts success- fully for the object's size, location, orientation, magnetic permeability and conductivity. For more general objects, the system determines the fitness of a candidate relative to a UXO being sought by comparing measured data with its signature.