When a perfectly electrically conducting (PEC) waveguide is perturbed by the insertion of a PEC structure aligned with its axis, its propagation constants are perturbed. The underlying boundary value problem may be converted to a homogeneous Fredholm matrix equation in which the propagation constants are found from the roots of the determinant of the matrix; stable and numerically efficient processes may be employed to find the propagation constants. There is no constraint on the size or shape of the inserts. As well as determining the empty waveguide parameters, this approach provides an estimate of the perturbation to the propagation constants of the empty waveguide.