Exceptionally strong enhancement of the Raman signal exceeding eight orders of magnitude for near-infrared (1064 nm) excitation is demonstrated for an array of dielectric submicron pillars covered by a relatively thick metal layer. The microstructure is designed to support ‘spoof’ plasmon-polariton excitations with resonant frequencies significantly below the fundamental surface plasmon resonance. Experiments reveal a relatively narrow range of spatial parameters for the optimal resonant scattering enhancement. They include a period close to the excitation wavelength, a specific ratio of the pillar planar size to the period, and optimal heights of both the pillars and the covering silver metal layer. The realized microstructures can be produced by fab-compatible photolithography techniques, and their outstanding sensing possibilities open the venue for the biomedical applications.