The phenomenon of tunneling is investigated for a symmetric double-well potential perturbed by a monochromatic driving force. The analysis is based on a numerical treatment of the quantum map that propagates the system over one period of the external force, and of the spectrum of its eigenphases (quasi-energies). At driving frequencies between the bare tunneling frequency and the harmonic well frequency, we find for specific parameter values of the driving force a localization of the wave packet in one of the wells (coherent destruction of tunneling).