Just go to MPD with your license and the car’s registration. I’m in Zone 5 and have family members who are on vacation and asked to leave their car with me for the time being, so even without a visitor actually staying with me, I was able to get a 15 day residential visitor’s parking pass, no problems. I had also called the 5th District station a couple days in advance and had spoken with an officer about this and both he and the officer that actually issued the permit said it was okay, so it seemed like this a known procedure. It may also be of note that my family left the car in the DCA parking garage (early, early flight) and I picked up the car with a spare set of keys that afternoon, so when I went to the police station, I didn’t even need the “visiting” owner of the car, as long as I still had the registration.
Of course, as soon as I got home with both the car and permit in hand, I received the permanent visitor’s parking permit in my mail. Bah.