We report the experimental observation of tunneling of slow and fast electromagnetic modes in coupled periodic waveguides shifted longitudinally by half of modulation period. According to the symmetry analysis, such a coupler supports two electromagnetic modes with exactly matched slow or fast group velocities but different phase velocities for frequencies close to the edge of the photonic band. We confirm the predicted properties of the modes by directly extracting their dispersion and group velocities from the near-field measurements using specialized Bloch-wave spectral analysis method.