Both are possible. 'Must' suggests logical certainty, 'might' possibility.
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wangqh2696122Mr. Mike is on time for everything. How did it come about that he was late for school this morning?” “He must/might have got stuck in a traffic jam on his way here.”wangqh2696122 ,
grammarfreakI personally would prefer "gotten" when used in the " auxiliary have" consturction.That may be fine in AmE. Only 'got' is acceptable in BrE.