Are there any good (preferably free) tools out there?
Can they give accurate estimates that reflect production results when the app goes live?
I would personally go with Apache Bench http://httpd.apache.org/docs/2.0/programs/ab.html
It's free, straight forward to use and lightweight.
If you are looking for a something a little more robust then I think Apache JMeter might be worth looking at. http://jmeter.apache.org/. Again, it's free, a bit of a learning curve and has a GUI so a little heavier.
You might also want to take a look at this Q/A Performing a Stress Test on Web Application?