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 $13.6\mathrm{GHz}$ spectral resolution over a $14\mathrm{nm}$ optical bandwidth, or a virtually imaged phased array spectral disperser, configured for $1.6\mathrm{GHz}$ spectral resolution over a $200\mathrm{GHz}$ 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.