It's often used to describe an answer that's no "real answer" in the sense that it lacks the decisiveness or definiteness that people expect. It's as though you were to say, "well, you know, everyone has a valid point and basically everyone is right, no extreme solution is good here". See, for example, this article, where the author is tasked with deciding whether one ought to write "kennenlernen" or "kennen lernen" and gives what he describes as a Solomonic answer, to wit, both are valid. http://www.neue-rechtschreibung.net/2011/01/25/kennen-lernen-oder-kennenlernen-die-salomonische-antwort/

Die einem Weisen eigene Ausgewogenheit und Einsicht erkennen lassend. An answer which is marked by its balance and wisdom, avoiding extremes, a tie-breaking third opinion. In German the term 'salomonisches Urteil' is used frequently, referring to a very just and wise judgement.