I have had a browse round Ukraineʼs IDN ccTLD укр and here are some of my observations.
① There are a good number of results for укр
https://www.google.co.uk/search?q=site:.укр
② Many redirect to an ASCII
③ Most use either English or romanised Ukranian for the pathname part of the URL. On a Linux box it is easy enough to have the pathname part in Ukranian Cyrillic whilst retaining the underlying original English/Romanised directory naming by using symlinks eg
ln -s category категорія
I did find one site which has the whole of the URL in Ukranian Cyrillic
http://прицепы.укр
http://прицепы.укр/прицепы-купить/одноосные-прицепы
http://прицепы.укр/спецприцепы/прицепы-для-мотоблока
http://прицепы.укр/спецприцепы/купить-прицеп-для-пчел
...etc...
André Schappo