UPS for modem and router?

[Lorin]

I've had it with losing my IP address every time the power goes out. A UPS will keep my connection alive (until the battery dies), but I'm wondering if I need to have both the modem and the router hooked up to the UPS, or just the modem, or just the router. Has anybody else gone down this road?

[NFtoBC]

You would need to power both. This assumes the local Telco office is not also without power.