Another way to get past the "May I say what your call is regarding?" screen is to ask a technical question that Frieda will not be able to answer. If you have done your homework, you should have access to the industry buzzwords that can make this a very valid inquiry, one the Guardian of the Gate would likely not know the answer.
The best way to do this is to ask a question that would further qualify your potential interest in the company. An example question for a Computer Science grad seeking to reach the Network Manager about networking positions might be:
"I needed to ask _____ what type of Cisco routers your company is currently using. Can you help me?"
Probably not. Once you get through to the Network Manager, you should still ask that question, then follow with how your background can potentially benefit them. For example:
"I recently received my Cisco certification and have been working with Cisco and Microsoft networks for the last two years, specifically supporting Cisco _____ routers. Is this the type of experience your company would usually look for in the area of Network administration?"
This technique is something of a gamble. But if used intelligently, it can launch you through to the Hiring Manager.