  A semiclassical formula for the coherent-state propagator requires the
determination of specific classical paths inhabiting a complex phase-space
through a Hamiltonian flux. Such trajectories are constrained to special
boundary conditions which render their determination difficult by common
methods. In this paper we present a new method based on Runge-Kutta integrator
for a quick, easy and accurate determination of these trajectories. Using
nonlinear one dimensional systems we show that the semiclassical formula is
highly accurate as compared to its exact counterpart . Further we clarify how
the phase of the semiclassical approximation is correctly retrieved under time
evolution.
