/diy/ - Do It Yourself

I have a little something I have been toying with recently.
My 1999 Ford Mustang uses a transponder inside the key in order to allow it to start. My research has yielded that it uses a radio chip in the key to signal to the receiver that it is OK to start the car.
I tested it with a key cut at a hardware store for my car and without the chip, it wouldn't turn over. However, when I hold my chipped key near it, it will turn over with the hardware store key. So it obviously has nothing to do with physical contact between the chip and ignition so it's all wireless. This means that there is a signal coming from the chip.
My question is, what would I need to do to intercept and duplicate this signal without a chip? And could it work on newer cars with push button starts? I think this could be useful for people who don't want to be raped by locksmiths charging 60$ a pop for cutting a key and pressing a button and even more so for new cars where a replacement key can cost multiple hundreds of dollars.
I am aware of some devices being used by high end car thieves but there is not much documentation on the technology that I've found.