Non-Overlapping Magisteria or NOMA was first poposed by the paleontologist Stephen Jay Gould in his book Rock of Ages.
Gould described described a "magisterium" as "a domain where one form of teaching holds the appropriate tools for meaningful discourse and resolution". And went on to develop his idea writing: "the magisterium of science covers the empirical realm: what the Universe is made of (fact) and why does it work in this way (theory). The magisterium of religion extends over questions of ultimate meaning and moral value. These two magisteria do not overlap, nor do they encompass all inquiry (consider, for example, the magisterium of art and the meaning of beauty)."
Beauty, as such, is an abstract quality which it is certainly impossible to measure scientifically. However, when people react to things which they consider beautiful this can be studied in the same way as all other aspects of our behaviour. We can say that something exists tangibly because some measurement of the state of the appreciation of beauty could be made in a brain scanner. Consequently, the human behaviour of reacting to what is felt to be beautiful can be studied empirically. And we can conclude that something tangible, or at least potentially measurable, correlates with beauty.
Criticism of NOMA
In reality NOMA gives religion a "get out of jail card for free card" when it gets caught out making real-world predictions. As Richard Dawkins has pointed out god either exists or he doesn't - and there is no reason that this hypothesis could not be tested in the same way as any other.
Furthermore the religious supporters of NOMA seem quite coy about where their NOMA line should be drawn. Religious beliefs are the basis of creationism, Intelligent Design and theistic evolution. While many science-friendly NOMA advocates happily attack creationism, they then hold the NOMA shield up to defend other (their own) religious beliefs - a position which could seem a little intellectually dishonest. Creationists are in any case not noted for intellectual honesty.