Abstract: The last two years are marked by a remarkable progress in the simulation of binary black holes. There is also substantial progress in developing theorems which establish the computational stability and well-posedness of symmetric hyperbolic systems. We present techniques that can lead to conserved quantities which suppress exponentially growing error modes. We also prove the stability and convergence of our code for periodic, Neumann, Dirichlet and Sommerfeld boundary conditions. A key issue is a valid treatment of the outer boundary, which imply the accurate preservation of constraints at the boundary. We introduce a new formulation of constraint-preserving Sommerfeld type boundary conditions, which can be used to enhance the computation of gravitational waveforms. The tests that are performed deal with an essential feature of the black hole excision problem, namely a non-vanishing shift. Although our application here is limited to a model problem, we expect these techniques to further the recent progress in the simulation of black holes by harmonic evolution.