We report experiments in which wavelength-parallel spectral polarimetry technology is used for measurement of the frequency-dependent polarization mode dispersion (PMD) vector. Experiments have been performed using either a grating spectral disperser, configured to provide 13.6 GHz spectral resolution over a 14 nm optical bandwidth, or a virtually imaged phased array spectral disperser, configured for 1.6 GHz spectral resolution over a 200 GHz band. Our results indicate that the spectral polarimetry data obtained via this approach are of sufficient quality to permit accurate extraction of the PMD spectrum. The wavelength-parallel spectral polarimetry approach allows data acquisition within a few milliseconds.