If they say, "you don't have to do that," listen very closely to HOW they are saying it. If they are a bit stand-offish, like "I don't want to give this person my contact information," then just drop it and look them up on Facebook a week later. Send them a friend request with a reminder of where you met. If you don't know their last name, try to get a call sheet (If they are a "green set" their call sheet may be on an iPad, and you'll have to use some detective work).
If they say it in a way that they are just being modest, say, "well, I've really enjoyed meeting you and would like to stay in contact. You never know when I may be able to help you connect with someone for another job you may be seeking, etc." Then ask for a card and if they don't have one ask if they'd like to write down their contact info or connect on Facebook.
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