Our technique for mixed quantum-classical simulations has the correct limiting behavior at short and long times. Two-state systems are used to investigate coherence effects and dephasing, and to compare with results from a simpler theory of nonadiabatic dynamics. Compared to fully quantal results, our method is shown to be accurate for a wide range of models over a wide range of energies. The two-state models do not explicitly include the bath dynamics which lead to dephasing, and the models do not include tunneling. These are above barrier scattering exercises for which the dynamics is fully coherent. We apply our theory including an arbitrary dephasing time scale, and quantitatively reproduce the correct results for long dephasing times and qualitatively reproduce the results for short dephasing times. We conclude that our method is applicable to relaxation and activated processes in condensed matter where the dephasing time is unknown. We propose that our method is appropriate for simulations of electronically and vibrationally nonadiabatic processes in solids and liquids.