Was he in the act of shooting?
 

I've been in a couple of situations where I had to basically "predict/guess" whether or not the player was indeed attempting to shoot (or pass) when he was fouled. I'd like to know how veteran officials handle this situation. Will it ALWAYS end up being a judgement call?

Judgement--it's why we get paid the big bucks. ;)

Act of Shooting?
 

I'm not sure about your "attempting to pass" situation, but on your "attempting to shoot when he was fouled", this might be to the point.
This is why I am trying to stamp out the all-too-cool-to-call phrase "On the Floor!" with me myself and my partners. True, a fouled player may not have yet become an airborne shooter, thus is still "on the floor", yet by rule he may deserve two shots at the stripe if his completed try was not successful if he was fouled.
Seems it's not so much a judgment call as it is a matter of identifying when the act of shooting begins. According to 4-41-1, "The act of shooting begins simultaneously with the start of the try..." and 4-41-4, "The try starts when the player begins the motion which habitually precedes the release of the ball."
A somewhat helpful site (to be used with caution, as with anything) which offers visual examples may be accessed at: How to officiate when a player is shooting in basketball | Video « Wonder How To (Caveat: this site features FIBA content and it sometimes has some erroneous video illustrations on some matters, but at least it served as a resource to begin me thinking about the topic at hand and prompt me to further exploration; I wish the "Officals' Ed." section of the NFHS website had a good set of video clips on this topic, or maybe I missed them there)
Judgment call? Perhaps. Yet there are some concrete indicators of how that judgment should be made more confidently.
Hope that helps you on a topic I'm continually studying, too.

I don’t think I really qualify as a veteran official, but here is my take on it.
Judgment, of course. Where the ball handler is looking and the direction the arms are going can be a good indicators. However, when in doubt, I usually go with the shooting foul.

Try studying rule NFHS 6-7-EXCEPTION(c). That tells you when the act of shooting begins for both a try and a tap.;)

Then it becomes a judgment call.

This is, of course, correct.

I went through a phase in which I was calling non-shooting fouls when the foulee was gathering the ball. This was not the "expected" call, and I heard about it. I also learned (by following JR's method) that I was applying the rule incorrectly.

I am not a fan of "always make the expected call," but it's worth reflecting on the situation if you're routinely not making the expected call. Expectations are often, though not always, correct.

Thanx for the Insights!
 

Excellent advice! That reference is spot on, and adds some good, descriptive phraseology not included in previous mentioned definitions. I just checked the definition of "Continuous Motion" and was reminded of more helpful insights found there. Putting all these references together in one place pretty much provides quite a conclusive case for when this judgment call can and should be made.
And though neither rulebook nor casebook use the term "gathering the ball", as was said by mbyron, that term does seem to adequately describe what all the references dictate, I think.
To which the opposing coach will complain, "No way he was in the act of shooting!" To which I will say to myself, "Get a book, coach."