We formulate and demonstrate experimentally the high-resolution spectral method based on Bloch-wave symmetry properties for extracting mode dispersion in periodic waveguides from measurements of near-field profiles. We characterize both the propagating and evanescent modes, and also determine the amplitudes of forward and backward waves in different waveguide configurations, with the estimated accuracy of several percent or less. Whereas the commonly employed spatial Fourier-transform (SFT) analysis provides the wavenumber resolution which is limited by the inverse length of the waveguide, we achieve precise dispersion extraction even for compact photonic structures.