I know http://www.xn--sknetrafiken-ucb.se, but like many it just redirects to an ASCII version. (Does it look weird seeing "Skane" when you know it ought to be "Skaane"?)

Similarly for a power company, http://xn--rsted-uua.dk, just a redirect, but they do use it on adverts and my electricity bill.

Some that don't redirect: http://xn--mgk--jra.dk/ https://www.xn---strm-uuae.dk/ https://xn--magnusbrth-85a.se/

(HN has converted the displayed URLs to Punycode, presumably as a quick security measure without reference to the reasonable characters for each TLD.)

rødt.no comes to mind, but I know I’ve seen others.

www.hörby.se

You probably don't want to remove the dots on that one.