A professor of mine explained the concept of CDMA to us, which is the way modern cell phones communicate. It's a spread-spectrum communication, and due to the way it works, it can pick the actual signal out of noise quite well. It was originally implemented in some war, and was extremely useful because the signal often does literally reside in or very near the noise floor, making it hard to detect, and was just about immune to being jammed by a strong narrow-band signal like traditional communication schemes.
You might be able to jam it, but you'd probably need a lot of power spread over a large spectrum, and by then your system would be so illegal you wouldn't dare turn it on :lol:
As a demonstration of the power of CDMA, we DO have a faraday cage at my university. And students have been able to make cell phone calls from inside... signal strength is of course reduced, but it still works. In all fairness, it is not 100% done construction as it needs improved earth grounding, but it is still a complete box where you are surrounded on all sides by two layers of sheet metal.