There have been numerous studies done by the US and NATO relative to the Russian Black Sea Fleet.
The thing to remember about the situation in the Black Sea, is that unless the US and/or NATO wish to go to full scale war with Russia, they cannot attack (unprovoked) the Black Sea Fleet ships. There is no need to have any US or NATO ships in the Black Sea, at least not in a military sense, unless the US and/or NATO are planning on imminent attack.
Plus, if the US and/or NATO wanted to attack/neutralize/destroy the Black Sea Fleet, they would not have to use naval forces to do so. Aircraft flying from land bases using air-launched anti-ship weapons (ie ~Harpoon, Tomahawk, HARM), along with surface ship and submarine launched Tomahawk cruise missiles, would clear the Russian ships from the open sea in very short order. Their only hope of having surface ships surviving any length of time would be to retreat to their harbours under protection of Russian Air Force and land-based AA systems.
In studies during the height of the later Cold War period, the best the Soviet Navy ever achieved was to have a significant number of its submarines survive past the death of their surface fleet. The best the Soviet surface fleet ever managed was to have 10% of its surface combat ships survive past 2 weeks. This was assuming that the Soviet surface navy sortied to attack the US and/or NATO surface and submarine units, while also helping their submarine fleet deploy under a protective umbrella. This was also assuming that it was a conventional war, and that there was some warning and therefore time for both sides to prepare.
As an added bit of info, the US all by itself (with some lead time) currently has the ability to deliver ~180 (or more) Harpoon and/or Tomahawk anti-ship missiles on target anywhere in the world on the open seas or in coastal waters. All arriving on target within a couple of minutes if so desired.