We did go to Tortola in 2005; not a scheduled port for that cruise, but Princess had to cancel our visit to Barbados because our ship had a problem with a holding tank and we left Antigua several hours late. Because of that, the captain took us to Tortola instead. It turned out to be a very good stop, as we were able to book a ship's excursion to "The Baths", which is on the island of Virgin Gorda, about 20 minutes away.
That was an excellent excursion that I would recommend if you are able to walk up/down moderately steep slopes. My travel complnion are both senior citizens and were able to do it with no difficulty.
The Baths is at a national park, and when you get down the hill to the beach, there are huge granite boulders that are on the beach and in the water, that came from an old volcano. The waves crash over tham and the scenery is beautiful. There is also sandy beach where you can lay in the sun and go into the water. The way the boulders are piled make some grottos that some make their way into.
If that excursion is offered, I would recommend it.
I canot recall if we tendered in Tortola.