When you're getting near "E" fill a gas can and take it with you. Then keep driving until you run out of gas. That's the only way to know for sure. A fuel gauge is a pretty crude instrument and different factors can effect its reading. You can park on a hill nose-down and run out of gas because the pump pickup is in the far rear of the tank. Typically, you're going to be down to a couple of gallons by the time the "Check Gauge" comes on, but not all if that is going to be usable.
I ran my tank down to change my fuel pump. I carried a can of gas with me just in case I ran out (I didn't). When I pulled the tank and emptied it completely, there was about 1 3/4 gals left in it. I have a 24 gal tank and according to the gauge and the trip computer, each division marking on the gauge should be about 6 gals and it seems to be fairly accurate. When I reinstalled the tank, I put in 12 gallons and the gauge registered exactly 1/2 on level ground. To be safe I never wait until the needle hits "E". I don't see the point, as you're gonna have to buy fuel anyway, but it's nice to know how low you can go just in case.