Is there any way to gauge the level of propane left in a tank for a BBQ grill?
If the tank is sweating, look at the sweat line.
Weigh a full tank, then weigh an empty one, then weigh your tank. You’ll be able to get a percentage of fullness based on the difference in weight.
There are two ways I know of. One is to pick it up and shake it. You can make a rough judgment of how full it is (e.g., 3/4, 1/2, 1/3, etc.). The other requires using it - in some temperature and humidity conditions, the portion of the tank with fuel in it will be covered with condensation.
I think Alton Brown, on a show about grilling, suggested pouring some hot (boiling?) water down the side, then feeling for the temperature change.
from http://www.goodeatsfanpage.com/Season6/Chops/Chops.htm
Can’t vouch for the accuracy.
They make stick-on strips that work on this principle.
Hot water poured down the side will show a distinct line where, if any.
You can also look for the weight - it’s stamped on the collar probably - for the “standard” propane tank, I think they are filled with 20 pounds of propane. The tare weight or T.W. is stamped on the side - which is the actual weight of the (empty) tank - so subtract the TW from the total weight to determine fuel level. After a while you can kinda tell just by hefting. Further, I think there are some actual decent gages available now.
Here is the solution to your problem:
That’s going to be the best way. Indeed, the standard barbecue tank is a 20 pound tank and the weight roughly doubles when the tank is full (I don’t remember the standard tare weight off the top of my head.) Filling a tank from completely empty to full should take about 4.7 gallons. Before the OPD made filling a propane tank pretty much brainless (at least for that size, other sizes do not have any sort of device) the only way to get a proper fill was to weigh it and then add the proper amount of liquid propane to get to the tare weight plus the weight of the max amount of propane. Any retail propane filler will have a scale that allows them to do that. A couple times I filled big bottles for local hot-air ballonists and also a couple RVs (those are interesting fills by themselves, but I believe those also have an OPD, and they did have a gauge.)
What makes it a bit tricky is that the other weight listed is not actually the propane capacity by propane weight but the capacity of water by weight (marked WC.) The density of liquid propane is roughly half the density of water. However, the actual capacity is only 42% of water capacity (to allow ample room for expansion into the headspace.) So a standard barbecue tank is marked at 48 pounds of water capacity, and the actual capacity is thus 0.42*48, which is 20.
Would you believe I actually had to take a test on all this stuff (as well as safety and some other regulations) before I could legally dispense propane in New Mexico? I’ve still got my (now-expired) certification card for laughs. Then I got lots of questions from customers about how I could take the smell of ethyl mercapatan (my standard reply was after you’ve smelled something like pyridine or thionyl chloride, ethyl mercapatan doesn’t seem that bad.)
open it up and look 
The hot water method works pretty well, you can feel where the level is.
I had one of these and it never seemed to work.
At one time they made grills with springs and gauges (scales) which showed the weight. I apparently installed mine upside down because it showed always full. Others I saw, however, seemed to work ok.
Do they not make grills with these scales anymore?
Bob
My Weber gas grill has one of these scales. Never worked worth a darn!
I use the hot water and hand method myself. And have a spare tank too.
Unlike GaryM’s experience, the scale on my Weber is a lifesaver. I’m never worried about unexpectingly running out of gas again. Sure, I know the other methods, but I’m lazy. I mean to ask Weber to send me an N.G. burner and run it to my gas line, but I’m too lazy to have done that yet :(.
Or you can buy a really cool Fiberglass Propane cylinder. link This is the brand that we sell where I work, they are pretty nice. We sell other parts for boats and marine systems, and aside from them being translucent so you can see the level of the fuel inside, they don’t rust and are not as heavy as steel tanks, and are less money than aluminum. Oh and they now come in several colors (at least the plastic cage)
The standard steel tank weighs 18 pounds empty, and roughly 38 pounds full. You can weigh the tank itself, but some scales aren’t so good near the bottom of their range. Weigh yourself, with and without the tank