How to do "But/However"

In all the Indo-European languages I've had a look at, "but/however" are
standalone words. In logic/semantics, "but" is considered yet another
"and". The difference in using "but" instead of "and" is that the "but"
says that something else was expected than what actually happened.

a) X and Y.
b) X, expected Y but got Z.

I'd hate to copy Indo-European usage here, so what other ways are there
to to get the effect of "but"?

I thought of using "and" as usual with the second clause (the Z) marked
with the counterfactual, but :) that seems wrong somehow. So I ask:

1. How do your conlangs handle but/however?
2. How do natlangs handle but/however differently from IE?
3. Searching for but/however is rather pointless, so is there a
   good linguistic term?


t.

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