I have ridden on occasion solo as captain and found that immediately after my stoker had gotten off, that the tandem became very sensitive in the steering until I got use to it. Should note that my stoker is heaver than I, so as I did the little steering corrections, I did not have the weight to dampen the feel. You get use to in in a couple miles though.
As far as braking goes do be careful. You just have to be aware and adjust your speed to compensate for lack of weight over the rear tire.
I do get comments such as "where is your stoker" or "your stoker is missing" and my reply is "Oh my gosh, did she fall off again?"
On various large rides I have seen inflatable life size dolls strapped in place back there. Always good for a laugh.