Electromagnetic material characterization is the process of determining the complex permittivity and permeability of a material. Rectangular-waveguide measurements involving frequencies greater than several gigahertz require only a relatively small test sample. In an X-band (8-12 GHz) waveguide, for example, sample dimensions in the cross-sectional plane are only 0.9 in by 0.4 in. However, waveguide dimensions become progressively larger for lower-frequency applications. Consequently, the larger quantities of materials are required, leading to possible sample-fabrication difficulties. Under these circumstances, a waveguide sample holder having a reduced aperture may be utilized to reduce the time and cost spent producing large, precision samples. However, this type of holder will cause a disruption in the waveguide-wall surface currents, resulting in the excitation of higher-order modes. This paper will demonstrate how these higher-order modes can be accommodated using a modal-analysis technique. This results in the ability to measure smaller samples mounted in large waveguides and still determine the constitutive parameters of the materials at the desired frequencies.