You can always use a cordless phone if the base is powered by a UPS, assuming that the provider is still working (for cable modems that would mean the cable is up and the modem/router is on UPS). If you have a POTS landline, the you would need the OBI and the cordless base to have power with a UPS.
A UPS is available at Walmart, Costco, Radio Shack.
An external unit I drew up uses a DPDT relay, a small power supply and some phone connectors and cords.