I think at one time they had a program at the aquarium where you could get in the water with the dolphins and learn more about them, but not really "swim" with them. I love going to the aquarium and to the inner harbor, great place!
As for actually swimming with the dolphins, we did this at Discovery Cove in Florida and it was GREAT! I think it was only like $200 per person and you spend an entire day at the park. They have a beach area, places to swim with the rays and incredbile looking reefs. they also include a nice lunch. The dolphin part is I think around 30-45 minutes long. You go out in a small group and they show you the different features of the dolphin. Then you do little "tricks" with him and when you get ready to come back to shore you grab on to his back and he takes you back to shore. Of course afterwards you can purchase photos and videos of your experience.
It is most definetly worth the trip down there! We are thinking of going down again soon.
Oh, since they are affiliated with Sea World, you get free passes to visit that park as well while you're down there.
www.discoverycove.com