Happened to me too on same car... Don't worry its the guage/sensor thats doing it. It is probably pretty expensive to get fixed... at least $300. So I just go by my trip odometer now. But slowly but surely its starting to fix itself... weird like that... It goes up when I fill tank up but goes down too fast and when its on empty i still have a good 50 miles left. But since the "Low On Gas" light has a weight sensor rather than the floating ball sensor used in the gas guage... which is probably the problem btw... the light will still come on when its time to fill up... and you usually have about 10-20 miles left at that point.

Hope this helps... my suggestion is move to trip odometer and save the $$. But its your call... oh and also come to think of it, since it happened to both of us its prolly happened to more people... and Honda fixes frequent problems like this for free... ask your dealer and they can tell you if you can get it fixed for free. I got my oil gasket replaced for free because of the same warranty thing that honda gives... even if the car is old and not original owner or anything...