Different dispersion properties are imparted to nonradiative dielectric (NRD) waveguides by split ring resonator metamaterials. Both longitudinal-section magnetic and longitudinal-section electric modes are capable of propagating very slowly due to the metamaterial bianisotropic effects, and can even approach zero velocity. Enhanced energy flow in the considered structure is also demonstrated under certain conditions. Finally, miniaturization of NRD waveguide based on these unusual properties is proposed.