We propose an extension of the well-known Makri-Miller model [J. Chem. Phys. 91 (1989) 4026] for the calculation of tunneling splittings of ground and excited states of symmetric double well potentials. Our approach is based on generalized trajectories which can penetrate into the classically forbidden region. The performance of the new method is demonstrated for a two-dimensional model potential. We compare our results with data from exact quantum mechanical calculations as well as from various semiclassical methods. The numerical effort is only slightly increased as compared to that needed for the Makri-Miller model. (C) 2003 Elsevier Science B.V. All rights reserved.