I play long tones first with no attack. The horn should speak on a whisp of air in all necessary registers. Then I check intervals to see if the entire system is in tune with itself. I do not play long passages, rather only short things that I have prepared well. Nothing to show off. Normally, I have a reference instrument with me to keep me grounded and open minded.
In a store or someones house, I have no chance to test "projection" or "power" so I don't. If there is a church or reasonably sized hall with good acoustics. near by, I try to take it there to test how well I hear myself when playing as well as other things needing space.
I always have a trusted second set of ears to also judge from the receiving end.