Jennifer, you may have some difficulty in actually renting such a car, unless you can find a company that does this. You see, if you pay an individual to rent his car and there's any sort of accident, he risks a huge liability, since his insurance company won't cover the car if it's rented out.
Best bet is to post a message on your company's or church's bulletin board asking if anyone knows someone with a classic car who would be willing to transport you to the wedding. (We're all only one or two steps removed from an antique car owner!) You could arrange to reimburse the owner under the table, or (if he / she was a good soul) simply offer to feed them at the reception afterwards. I've heard of people doing this sort of thing just for the fun of it. If any sort of liability is incurred during the process of moving you, the car's owner simply reports to his insurance company that he was doing a favor for a friend, not renting his car out.
You might also contact your local AACA (Antique Automobile Club of America) region, and ask them if any members are willing to do this sort of thing. You'll find a list of local AACA's at the website
http://www.aaca.org/regions/list.aspx . Not guaranteed to work, but it's a possibility.
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