Now here is a topic I can answer somewhat intelligently on. I am an RF Engineer for a major US based cellular company (hint: the biggest one) so this is a little up my alley. First of all, most US based cellular networks operate in the 800 MHz range. These phones/networks pose no danger to aviation systems, air traffic control systems or navigational systems.
However, some networks in the US and many in Europe and other places operate in the 1900 MHz range. These devices may interfere with the TCAS (anti collision) systems in some types of air craft. Most TCAS systems operate around 1095 MHz but there are some that operate at 2085 MHz and there is a slight possibility of momentary interference from a 1900 phone. That said I have never heard of a single instance where that has happened.
I agree with Meta, it always surprises me you can even get coverage in an airborne airplane. First of all, the cell sites generally do not have a high power output. In an urban area ERP is usually between 1 to 10 Watts max (30-40 dBm). Because there are usually a lot of cell sites you don't want any one handling traffic in the coverage area of another one. To further shrink the footprint of the cell we downtilt the antennas a few degrees so they are angled slightly towards the ground. This means that a handset in an airplane is receiving off the back lobe (reflection from the antenna rear) which in most antennas is less than 30% of the main lobe power. So if a cell has an ERP of 10 watts the back lobe will be at best 3 watts. Its no small feat for a 3 watt transmission to travel through 4 miles of air (which has clouds, several thermocline's, and other interference) to the airborne handset. Further, most handsets have a max power of 0.3 watts so it is even LESS likely the handset can get back to the cell.
Because of the physics of radio wave propagation (I'll give a more detailed explanation if needed) an 850 MHz signal will travel farther than an 1900 MHz signal with the same ERP. So if your phone even works in a plane, it's probably an 800 MHz anyway so there is no need to worry.