Filing a nonresident Michigan income tax return and entering $0 for MI wages is the correct answer.
Generally it is also a good idea to file the MI return by mail along with a copy of your IL resident income tax return, all your W-2s and a note explaining that MI was withheld in error. You can e-file federal and IL.
You don't have to do this, but MI may send you a letter saying why did you report $0 wages when your W-2s say $xx.xx? Then you would have to write a letter and send a copy of your IL return and your W-2s. That may not happen.
If you do mail MI, we suggest sending it by certified mail with return receipt so you have proof of delivery.
If you entered $0 on the MI return, your MI refund should equal the entire MI tax withheld on both W-2s.
If you mean that total refund is less, that is probably correct. The IL tax rate (4.95%) is higher than MI (4.25%) so you are paying more tax to IL on the MI W-2s than was withheld.
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