In this paper, numerical simulations are made, using the three-dimensional restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Saturn in the orbit of a comet. To show the results, the orbit of the comet is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct and hyperbolic retrograde. Then, the modification in the orbit of the comet due to the close approach is shown in plots that specify from which group the comet's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters (position and velocity at the periapse) vary is performed and the influence of each of them is shown and explained. The result is a collection of maps that describe the evolution of the trajectory of the comet due to the close approach. Those maps can be used to estimate the probability of some events, like the capture or escape of a comet. An example of this technique is shown in the paper. (C) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.