Modem power supply
I have seen that most of the external modems use an AC power supply, probably because is easier to find from different suppliers and because you don't need any care about polarity.
If you need to supply the modem with a battery or a power supply with a DC voltage, it is easy, because most of them take the rectified voltage ( usually 9 Vac that becames about 13 Vdc after the rectifier and the capacitor ) and regulate it to 5 V dc through a 7805 or a LM2575 ( depends on the brand of the modem ).
For this reason any voltage among 9 and 14 Vdc will be OK to supply your modem.
BTW, don't care about the polarity at the power socket.
Of course this is true only if the modem is AC powered.
Mandi