In this paper we consider a wave equation on a bounded domain Ω of Rn, with non homogeneous boundary Dirichlet data g supported on a part of the boundary, and we prove an observability estimate of this data from the rest of the boundary. This result is obtained under a geometrical condition on the part of the boundary supporting g to be compared to the so-called Geometric Control Condition of Bardos-Lebeau-Rauch, and on a pseudo-differential condition on g. The proof relies on microlocal arguments and is essentially based on properties of microlocal defect measures.