The instanton or stationary-phase formula has received much attention recently as a way of determining transition paths in reacting systems. In this paper, we analyze the instanton approach for some one-dimensional problems and compare the results it gives with data from a numerical simulation. We show that a proper comparison of the analytic and numerical results must take into account the boundary conditions used in the numerical simulations and also suggest values for the integration constant in the instanton formula that gives the best agreement with the simulated results.