Hello… my name is (your name)’s refrigerator. He/she isn’t home right now to take your call. To leave him/her a message, speak very slowly so I can stick the message with the help of these refrigerator magnets.
This isn't going to work for all carriers. On mine (AT&T), calling my own number dumped me into the audio voice mail menu and didn't record. You could always try calling the person on the other line again—you'll go directly to their voice mail, certainly. They could send you the recorded "voice mail" conversation after. However, that's not something most interview subjects want to get involved in.

RecordiaPro has options for recording both in the US alone (starting at $29.99 for 120 minutes) or worldwide ($40 for 190 minutes). Create an account before you call, put RecordiaPro's number in your contacts, and use it when you call out or silently add RecordiaPro to existing calls. For $36 per year, it will provide a number you can hand out to take future calls that get auto-recorded. Future recordings are available in your account.
If you’ve already created a custom voicemail on your iPhone, you can tap Play to see how your voicemail sounds. If you’re interested in creating a new message, tap the Custom button. From here, you can start recording your message by tapping Record and tapping Stop whenever you’re finished. Once you’re finished recording, tap on Play to make sure the message comes across as you’d like and hit Save (in the upper right) to save it as your voicemail.