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Propagation of tangential electromagnetic modes in array of split-ring resonators deposited on a thin dielectric plate is analyzed by studying the Fano resonance and electromagnetically induced transparency, which appear in the transmission spectra due to the coupling of these modes with the third plasmonic mode of the split-ring resonators. We determine the spatial dependence of the electric and magnetic field enhancement in these systems, showing a noticeable difference between diffracted modes in free-standing resonators and guided modes in the presence of a dielectric plate. We find that in the case of a subwavelength dielectric thickness, the in-plane modes are guided by both interference and internal reflections of diffracted waves. Numerical simulation is confirmed by analytical modeling and experimental data.