Shooting down a low observable aircraft or missile is a very dicey proposition at best and it involves a lot of new technology and usually a bit of luck on top.
The ability of any radar to detect a stealth plane is dependent upon a number of factors, including frequency (inverse of wavelength), radar pulse characteristics, receiver and signal processor capabilities, effective radiated power (ERP), signal to noise ratio (SNR), and, if an operator is in the loop, that person's awareness.
Search radars and fire control/tracking radars usually have vastly different operating characteristics, since the search radar is designed to search a large volume around the protected land area or ship and the fire control/tracking radar is designed to track the enemy plane/missile and provide a signal for the your surface to air missile to home in on. Search radars are even subdivided into surface and air sub catagories. The surface radar is designed very differently from the air search radar, since it must operate near the surface of the sea or land, a different environment than free space, filled with land clutter that messes up the picture.
Virtually any air search radar can eventually detect a stealthy aircraft when the plane gets close enough. The same holds true for a fire control radar. Eventually, you will be able to track the enemy stealth plane. The issue really is...can you detect, develop a viable track and guide a missile or AAA gun to the guy before he launches a weapon at you? That is the dicey part. They are not invisible...just very hard to see. The harder they are to see, the later you get to shoot at them...and the better chance they have of nailing you. I have no idea how the F-117 was shot down but I'll bet it was a mix of new technology on the part of the Serbs, with maybe just a bit of over confidence on our part.
[soapbox]