Most of our local news stations have started streaming severe weather coverage or breaking news so we watch it on a laptop if we have to go to the safe room or we lose power. I don't know how long my router and modem will run on the UPS but it seems to be quite a while. The broadband router has dual internal battery backups so it's good for hard wired use for about 16 hours after the UPS dies.

I'm going to watch this thread though. A handheld television would be a bonus but a small, simple LCD television on a UPS with a digital antenna would be easy enough to set up.

ETA: It looks like a USB Digital TV Tuner attached to a laptop might be an inexpensive way to achieve this although most appear to be wired. They seem to be available at the regular tech outlets although reviews appear to be mixed.