This research addresses the problem of the optimal interception of an optimally evasive orbital target by a pursuing spacecraft or missile. The time for interception is to be minimized by the pursuing space vehicle and maximized by the evading target. This problem is modeled as a two-sided optimization problem, i.e. as a two-player zero-sum differential game. This work presents a recently developed method, termed "semi-direct collocation with nonlinear programming", devoted to the numerical solution of dynamic games. The method is based on the formal conversion of the two-sided optimization problem into a single-objective one, by employing the analytical necessary conditions for optimality related to one of the two players. An approximate, first attempt solution for the method is provided through the use of a genetic algorithm in the preprocessing phase. Three qualitatively different cases are considered. In the first example the pursuer and the evader are represented by two spacecraft orbiting Earth in two distinct orbits. The second and third case involve two missiles, and a missile that pursues an orbiting spacecraft, respectively. The numerical results achieved in this work testify to the robustness and effectiveness of the method also in solving large, complex, three-dimensional problems.