Electromagnetic material characterization is the process of determining the complex permittivity and permeability of a material. A new waveguide material measurement technique is developed to reduce test sample size requirements for low-frequency applications. Specifically, a waveguide sample holder having a reduced aperture is utilized to decrease the time and cost spent producing large precision test samples. This type of sample holder causes a disruption in the waveguide-wall surface currents that results in the excitation of higher-order modes. This thesis will demonstrate how these higher-order modes can be accommodated using a modal-analysis technique, thus resulting in the ability to measure smaller samples mounted in large waveguides and still determine the constitutive parameters of the materials at the desired frequencies.