There are SIM card readers. (Walmart, in the camera battery area, carries a SanDisk reader that reads, among just about every kind of card made, SIM cards. It's about $17.) But if the card is unreadable, you may bot be able to read contacts or things like that, just files (including the one the contacts are in) with
PhotoRec (don't let the fact that it's free and FOSS - there are companies that wouldn't think twice about paying $500 for one use of the program. If the file is on the card, hard drive - any storage device that the computer can see - PhotoRec will find it and recover it, even if the filesystem is destroyed. (Think lost accounts receivable - you either run PhotoRec or file for bankruptcy, so the app can end up being worth a fortune.)
You should be able to figure out what to do from
the step by step guide. (I'd advise telling it to read the whole card, not just the empty areas, and to take it out of Paranoid mode.)