The authors have used high resolution IUE spectra from their own studies and from the archive to examine the Mg II h and k chromospheric emission cores of a sample of late-type dwarfs and giants. Sharp photospheric absorptions were used to provide a velocity rest-frame with respect to each stellar photosphere with the IUE-limited precision of ±4 km s-1. The knowledge of the kinematics of the local interstellar medium (LISM) could then be used to identify cases where either the cores or the wings, or in best circumstances both features of the chromospheric lines were uncontaminated by LISM absorption. The authors derive, using only LISM-free emission wings, accurate Wilson-Bappu relations for both the h and k line, characterized by a slope higher than in previous determinations.