May have –ed:   Here the speaker makes a present supposition about the pre-present or past.

• He is late. ( or he was late).  He may have been delayed by the rain.  (One of the possible explanations of his lateness is (was) that he has been delayed by the rain.)
• A : I wonder why she didn’t come to the party.
• B : She may not have been well. (OR)  She might not have been well.
• A: I wonder why she didn’t say hello.
• B: She may not have seen you.

Might have—ed (1)  Here the speaker is, very hesitantly, making a present assumption about the pre- present or past.

• He is late .(or He was late).  He might have been delayed by the rain or he might have had an accident.  (Perhaps there was an accident, perhaps not)
• What he said might have been the correct answer.
• He might not have located the house.  Because the route-map was not taken by him.  It is still lying on the table.

(2)  To mention that something was possible to have happened although it did not in fact happen.

• A lot of men died in the accident who might have been saved.( There was a chance to save them though it did not take place)
• I daren’t think about what might have happened.( i.e Fortunately nothing  unpleasant happened! I don’t have even the courage to think about what could have possibly happened)
• Things might have been so different.
• You were lucky.  You might have been killed.( Obviously the person addressed is not dead, the chances of his being killed were considerable)

(3) You know the answer.  You might have told me. (Here, the speaker is expressing regret at not having been told sooner)

(4)  Sometimes ‘ Could ‘ has a similar meaning of ‘ May ‘ or  ‘Might ‘.

• The phone is ringing .  It could be Renz. (or It may/might be Renz)
• You could have left your umbrella in the shop. ( You may have/ might have left it…)