The best way to get past the Guardian of the Gate is to avoid her altogether. The 7:30/12:30/5:30 Rule states that if you call early in the morning, during lunch, or late in the afternoon you will likely get someone who is not nearly as good at screening as the person who normally screens the calls. You can often gather all the information you need, since this person is not a true Guardian of the Gate.
Remember that extension number you asked for? Many companies now have automated call forwarding which allows you to enter a person's extension during the off hours. That extension number can usually put you through directly to the phone on the manager's desk.
This is also an excellent approach in reaching a Hiring Manager who has been hitherto inaccessible. Why? Because if you are in management, you likely start early, work through lunch, or work late (or possibly all three). Many managers end up answering their own phone at those times. For all they know, it's their spouse calling to ask them to pick up something on the way home.
P.S. If you are calling a different time zone, make sure to adjust your timing accordingly.
After hours is the best time to reach a busy manager.
P.P.S. This is also a great way to reach a Vice President or even the President of the company. Keep The 7:30/12:30/5:30 Rule handy for future reference—you may need it in your career when you find yourself reaching higher within a company.