A Dutch friend of mine just took this ferry in the Georgia→Ukraine direction so I asked him for some details:
- Company name: UkrFerry
- Ship name: Greifswald
- Quoted boarding time in Batumi: 10pm
- Actual departure time from Batumi: ~ 8am
- Quoted duration of trip: 60 hours
- Actual duration of trip: ~ 55 hours
- Price: USD $170 for a bed in a 2-bed cabin
There were also 4-bed cabins that were only a few dollars cheaper.
Apparently nobody at the office speaks any English and even when taking a Georgian friend to help a lot of details including which night the ferry departed were very unclear - so be prepared! For instance he was told to be at the ferry at 10pm but it didn't actually leave until about 8am!
There are three good quality meals per day included in the price but nobody speaks English. All announcements etc are in Russian only.
Also there is nothing at all to do on the ferry. Just one TV which is in Russian, and it's hard to go above deck.
Thanks very much to Rowan for letting me grill him. I'll add some photos later if possible after his crossing.