This paper is devoted to the numerical computation and continuation of families of heteroclinic connections between hyperbolic periodic orbits of a Hamiltonian system. We describe a method that requires the numerical continuation of a nonlinear system that involves the initial conditions of the two periodic orbits, the linear approximations of the corresponding manifolds and a point in a given Poincaré section where the unstable and stable manifolds match. The method is applied to compute families of heteroclinic orbits between planar Lyapunov periodic orbits around the collinear equilibrium points of the Restricted Three-Body Problem in different scenarios. In one of them, for the Sun-Jupiter mass parameter, we provide ranges of energy for which the transition between different resonances is possible.