A nondestructive technique for determining the complex permittivity and permeability of a perfect electric conductor backed magnetic shielding material using a dual waveguide probe is presented. The dual waveguide probe allows for the simultaneous collection of reflection and transmission coefficients which distinguishes it from single probe methods common in the literature. Theoretical development of these coefficients, which is accomplished through a coupled magnetic field integral equations formulation using Love's equivalence principle and solved via the method of moments (MOM), is discussed. Evaluation of the resulting MOM impedance matrix elements is performed using complex plane integration leading to enhanced computational efficiency and physical insight. Comparison of the theoretical and measured reflection and transmission coefficients using a root finding algorithm leads to the desired permittivity and permeability. Measurement results of a magnetic shielding material are presented and compared to traditional methods for the purpose of validating the new technique. The probe's sensitivity to aperture alignment, sample thickness, and flange thickness is also investigated.