Given that I must address a university by abbreviation, say call the University of X simply X, for some given X, and that there is no official abbreviation for the name of this university, what is a safe strategy to call this university?
Do not do this. Especially since there are often many smaller universities that you do not know about that partially or entirely share the same name. For example, does "Rochester" refer to University of Rochester or Rochester Institute of Technology? Does "University of Massachusetts" refer to the well-known research campus in Amherst, or the very distinct and semi-separate institutions in Lowell, Boston, Worcester, or Dartmouth?
If you are forced to, ask Wikipedia, which will generally have an accepted shortened version in its article (e.g., "UMass Amherst"). If there is no Wikipedia article, then it's definitely not notable enough to abbreviate.