You should/ought to have told me that you were so ill. I wouldn't have asked you to do that difficult job.
should have -ed
ought to have -ed
They must have had an accident. It's 10 o'clock and they haven't arrived yet.
must have -ed
She was in the area, so she may/might have seen the accident.
may have -ed
might have -ed
I could have bought the tickets, but I thought that Anne was buying them.
could have -ed