I agree with blue85. I am in fact an alumnus of both Michigan (undergraduate) and Cornell (graduate), and the resemblance between the two is striking. Perhaps it is because Cornell was co-founded by a Michigan professor (Andrew Dickson White), who also happened to be Cornell’s first president from 1865-1885. After White, another 5 Michigan men (alums and/or faculty) held the position of Cornell president. I would say that Cornell is Michigan’s most similar peer.
But many other universities resemble Michigan in quality and prestige. Here are a few of them:
Northwestern University
University of California-Berkeley
University of California-Los Angeles
University of Pennsylvania
University of Texas-Austin
University of Virginia
University of Wisconsin-Madison