Are there ferry connections across the Black Sea?

Options are very limited. The only currently documented regular line is Varna–Batumi (Georgia), operated by Ukrferry; the current schedule mainly covers freight, and the operator publishes the passenger-service status on ukrferry.com — check with them directly before planning a trip. From Burgas itself there is no regular international ferry line; the Morska Gara (sea terminal) in Burgas port serves as a cruise terminal with a marina and coastal connections, for example to Sveta Anastasia Island. Details and links in our link directory.