  We discuss how to compute certified enclosures for the eigenvalues of
benchmark linear magnetohydrodynamics operators in the plane slab and
cylindrical pinch configurations. For the plane slab, our method relies upon
the formulation of an eigenvalue problem associated to the Schur complement,
leading to highly accurate upper bounds for the eigenvalue. For the cylindrical
configuration, a direct application of this formulation is possible, however,
it cannot be rigourously justified. Therefore in this case we rely on a
specialized technique based on a method proposed by Zimmermann and Mertins. In
turns this technique is also applicable for finding accurate complementary
bounds in the case of the plane slab. We establish convergence rates for both
approaches.
