Should I contact the person I was in a fender bender with after the accident?

I was in a fender bender. My car had no damage, but theirs had very minor damage. I called the police, but they never showed up. The other driver waited with me for a while, but then got inpatient and left. I did not get all of their information before they left. I would like to do as much to protect myself as possible. Should I call them to get their information over the phone, or should I just wait to see if they pursue anything? They have my phone number as well.