Accurate duct acoustic propagation models are required to characterize and reduce aircraft engine noise. These models ultimately rely on measurements of acoustic impedance for candidate materials used in engine nacelle liners. This paper seeks to increase the frequency range of normal incidence acoustic impedance testing in square ducts by extending the standard two-microphone method (TMM), which is limited in bandwidth to ranges where only plane waves propagate, to include higher-order modes. The modal decomposition method (MDM) presented includes the first four normal modes in the model of the sound field and thus increases the frequency range from 6.7 to 13.5 kHz for a 25.4 mm square waveguide. The MDM characterizes the test specimen for normal-incident and oblique-incident acoustic impedance and mode scattering coefficients. This paper first formulates the MDM and then applies it to the measurement of the reflection coefficient matrix for a ceramic tubular specimen over the tested frequency range of 0.3 to 13.5 kHz. The experimental results are consistent with results estimated from the TMM for the same specimen to within the 95% confidence intervals for the TMM, but the MDM provides data at higher frequencies.