The two call system is for confirming an incall appointment, not for screening.  There are many variations.  My experience has been a little different from Tokai's.

I usually make appointments several days in advance.  The lady asks me to confirm on the day of the appointment (1st call).  If I don't have them already, she gives general directions to her location and asks me to call when I'm close (2nd call).  Then she gives her unit number or street address or whatever else may be necessary, and as Tokai said, she might ask you to wait if she's not ready.

As far as what kind of screening procedures are used, it varies greatly.  Some ask for very little info; some ask for a lot.  One I saw must have access to a Private Investigator site or something.  While we were on the phone, she was pulling up addresses from some database, trying to confirm who I was.  That was a little scary, but she's very professional and well known.  I trusted her to be discrete.

Thanks, Tokai! I figured it was something like that, but in this milieu, I didn't want to take anything for granted!