Sump pump battery backup
The best plan I saw suggested in another question was to get a second 12V based pump. Place (or adjust) it so its start sensor is higher than your AC-powered pump, and also connect the battery to a battery maintainer. You get several benefits:


If the power goes out, the second pump will kick in when the water reaches it (which should be within about an inch of when the first pump would've started)
If the first pump dies, the second pump will still operate independently
If the inflow exceeds the capacity of the first pump, the second pump will augment the pumping capacity when the water reaches it (so you'd have both pumps running together).