They'll do it just using your phone #. And it's a good idea--we do it all the time now and carry it with us to each restaurant.
So far, we've only had to use it once--that was at Wolfgang Pucks when they had booked a private party several months previous and failed to let us know. The podium hostess was giving us a really hard time--until I whipped out the print-out (which had been printed only the day before). That changed everything. She became as pleasant as could be and called the manager at Portobello directly and got us seats there.