A receeding shoreline may provide as much as 5 minutes warning. This and a bunch of nteresting and important facts are included in a Nation Geographic News article, The Deadliest Tsunami in History?. I specifically found it interesting that they may only be a foot tall in the open ocean and only gain height as they reacg the shallows near shore. This can make predicting difficult. Also, it actually a series of "wave trains," with the first wave not neccessarily being the worst wave.

There's also a link to a special tonight:

Tsunami on the National Geographic Channel
Watch the documentary Tsunami: Killer Waves on the
National Geographic Channel Channel tonight at at 8 and 11 p.m. ET, and again on January 14.