0 The Theory:
You should put a comma before but only when but is connecting two independent clauses.
When you don’t have two independent clauses, leave the comma out.

1 and its application:
"The repeated auxiliary verb is not needed, but perfectly correct."

I think there should not be a comma before but because the subject is missing in the 2nd clause. Am I right?
- or is this an obvious omission (elipsis) and therefore there should be a comma?

2
"Your car is bigger than mine is. is also correct: the repeated auxiliary verb is not needed, but it is perfectly correct."

In this case, there should be a comma before but.