The detection of gravitational waves by ground-based laser interferometers, such as VIRGO or LIGO, or in space with LISA will be greatly facilitated by having a prior theoretical knowledge of the signal. In this thesis, we are interested in the most likely source to be detected by the first generation of observatories: a binary system of compact objects. More precisely, we consider, in the general relativity framework, the last orbits of the inspiral phase. It enables us, not only to provide realistic initial data for the merger simulations but also to obtain many informations on the compact objects themselves.A special effort is devoted to the improvement of those initial data, to make them as realistic as possible, from an astrophysical point of view. We thus built the first sequences of binary strange quarks stars, and this for various equations of state. Contrary to the case of polytropic neutron stars, the sequence ends at the dynamical instability. We have also calculated configurations of binary neutron stars using a waveless theory going beyond the commonly assumed approximation of a conformally flat spatial metric. We expect the obtained solutions to be more realistic and to be valuable new initial data. Finally, we studied various inner boundary conditions, in the single black hole case and for binary configurations. Those boundary conditions are based on the isolated horizon formalism and include some prescriptions for quasi-equilibrium.
