Radio-frequency quantum engineering of spins is based on the dressing by a nonresonant electromagnetic field. Radio-frequency dressing occurs also for the motion of particles, electrons, or ultracold atoms, within a periodic spatial potential. The dressing, producing a renormalization and also a freeze of the system energy, is described by different approaches: dressed atom, magnetic resonance semiclassical treatment, and continued-fraction solution of the Schrödinger equation. A comparison between these solutions points out that the semiclassical treatment, to be denoted as the S solution, represents the most convenient tool to evaluate the tunneling renormalization of ultracold atoms.