The low-temperature dielectric relaxation of collagen and elastin was studied over a wide range of hydrations h. The hydration-shell response increases weakly with temperature, is thermally activated, and conforms to energy barrier scaling. This demonstrates the existence of a decoupled, secondary relaxation akin to that in binary structural glasses. Indications for fragile-to-strong transitions and other changes of mechanism are not found for hydrated collagen and elastin. For low h, the dielectric strength increases superlinearly with h; concomitantly, the water molecules trigger significant mobility of the protein surface.