The main task of numerical relativity for gravitational wave astronomy is to calculate waveforms from inspiraling compact objects. One of the sources of systematic errors in these computations comes from boundary effects. These appear as a consequence of us truncating the physical domain and using (often naive) artificial boundary conditions at a finite distance from those compact objects. In my talk I will explain the ideas behind the use of compactified hyperboloidal coordinates to solve Einstein's equations in generalized harmonic gauge. This is an ongoing research program with the aim to include null-infinity directly in the computational domain, which will avoid completely such boundary errors.