It may also be possible for the name to have descended from a certain Michael's son given the name MacMichael - the son of Michael. Tracing the original Michael's clan affiliation may be nigh on impossible.

There can be a good deal of uncertainty in Scottish surnames, for instance:
"Sir Walter Scott tells us that one of his friends, shooting in the north, had a guide assigned to him under the name of Gordon. But he recognised the man as having served him in a similar capacity some years before in another place under the name of Macpherson. On asking the man whether he was not the same and whether his name had not then been Macpherson, the composed reply was, Yes, but that was when I lived on the other side of the hill."
Black, 'The Surnames of Scotland'