Electronics 2000

Frequent mains power failures makes me consider purchasing a 70Ah car battery to briefly power my 12V DC Router during an outage.
The Router requires a 1Amp input. I have always been told that a device will only pull what it needs so presumably know problem there.
However I have also been told that a 12v 70Ah battery will actually chuck out 13.2V if only delivering 1 Amp.
Don't want to risk frying my router so:
Is that correct and would a resistor in series in the positive line deal with that?
If so what value should the resistor be?
If not what should I do - or is the whole idea stupid?

The battery voltage should be over 12.6 if fully charged 13.2 is a bit high must be a brand new batt. It will be higher when on charge some smart chargers put out 16.5v for a short time ... most regulate at about 13.5.
You need a voltage regulator which regulates at your chosen voltage... perhaps a zener diode in series with a resistor, the voltage dropped by the resistor is resistance x current so a 13 ohm resistor will drop 1v ish, take your supply from each side of the zener diode.

Sorry 1 ohm in series with the diode will drop 1v across the resistor... achhhheeeeeerrrm.

Read your reply (and the hasty correction).
Then tried it out. Brilliant. Am now on line via my battery powered router. Your advice greatly appreciated.
It has inspired me to have a go at building a power regulator with variable resistor.
My birthday today so when I am in the Pub tonight I'll raise a glass to you!