Since Civil War period balls are held at some events and have a high degree of popularity with a goodly number of groups, I decided to give the activity a look-see. I'm amazed at how deeply you can involve yourself with aspect of the hobby. Actually, it's a hobby unto itself.
The Victorian Dance Ensemble is a very well put together group of Civil War period dance enthusiasts. They're heavily involved in preservation efforts and host a ball for that purpose. They also do demostrations and give dance lessons throughout Maryland and Pennsylvania areas. They sound like a bunch of fun!
In the same vein, the Commonweath Vintage Dancers are a group based out of Rhode Island and Massachusetts areas. This site is very well written and has a great overview of dance and dances during the Victorian period. They not only Civil War, this group dances in a variety of periods. Their favorite period appears to be the later 19th century.
Another worthy mention for the information contained on their site, which hasn't been updated in some time, is the Vintage Dance Society.
If you would like some personal lessons in the fine art of Civil War period dnace, then Our Wedding Dance, Inc. can teach you how to be light on your feet. If you look closely, one of the Bohemian Brigade, James Allen Davis, is apparently is cultivating his own style.
This post would not be complete with mentioning the 21st NC Infantry, who also does a bit 'o dancin' and was my inspiration for this post.