A periodically driven two-state dynamics, being analysed within the Floquet formalism, exhibits localization of the amplitude dynamics in an infinite frequency range, extending from the bare tunnel splitting up to infinity. In contrast, the suppression of tunnelling in a driven symmetric double well is restricted to a limited frequency regime, extending from the bare tunnel splitting up to the first resonance frequency with higher-lying states. With the amplitude dynamics of a periodically driven two-level system not being restricted to describe coherent tunnelling transport only, the localization phenomenon within the infinite frequency range does allow for novel applications for systems in strong laser fields.