Is it possible to make a cell phone transmit arbitrary radio waves at a certain frequency? Or does the Mobile OS only allow higher level access?
If the answer is 'no' as I expect it is, is there any way to make a phone talk to another electronic device remotely without handshakes and the like?
Probably not - as EFraim indicated, there'll be regulatory frameworks in place to say that devices of type A must use frequencies in the range X-Z with no more than a certain power output.
Additionally there's physical issues as well as to be able to broadcast at different frequencies requires different length antennas, certainly if you wanted to broadcast in the UHF range, the length of antenna would be radically different to the microwave-range that mobiles use (2.4GHz). Failing to match the antenna to the frequency can produce all sorts of odd effects that can destroy the output circuit.
Thus the only items available are going to be those that the phone itself presents - namely bluetooth and infra-red (if it exists). Some phones also have WiFi as well, so it really depends what you actually need this for.