As for any multichannel scattering problem, variational techniques can be utilized in the determination of the elements of the scattering matrix or of the equivalent network elements for a gyromagnetic obstacle in a waveguide. As always, however, it can be quite difficult to interpret numerical results which in general are neither upper nor lower bounds. A variational bound originally developed for the determination of the phase shift for a given angular momentum in a quantum mechanical central potential scattering problem is here adapted to the solution of a transversally magnetized, lossless ferrite slab in a rectangular waveguide propagating only one mode, the TE10 mode. With a simple trial function and with the aid of a comparison scattering problem which need not be tensor in character (so that the determination of upper and lower bounds is not really difficult), close bounds are obtained on cot ηe and cot η0, the cotangent of the real uncoupled phase shifts associated with the even and odd standing waves, respectively. The bounds obtained on cot ηe and cot η0 determine bounds on the equivalent π network. A second variational bound, which can be simpler to apply and which can be applied to a wider class of problems, is also developed. This too is an adaption of a formalism originally introduced in quantum mechanical scattering problems, and depends upon a consideration of the spectrum of the fundamental operator of the theory, the Hamiltonian in the quantum mechanical case and an analogue thereof in the electromagnetic case.