I had same problem with my 2002 XKR. Replaced tank & sensor for around $100. Got my aftermarket from PartsGeek.com

 

Several months ago, I bought a new tank for my 2003 4.2L car, because the old one was cracked/leaking and I was getting the low coolant warning, even with the tank full up. After several weeks, I got the low coolant warning with the NEW tank. Rather than returning it, I bought a new level sensor to save the trouble of installing the tank twice. The sensors are relatively inexpensive - about $25 for a Uropart or $40 for the OEM LNA5740AB. Have not had any problem since. I was using a good OEM tank cap (not the one that came with the new tank - did not fit tight enough: Eurospare tank BTW), so level is staying right at the filler neck. If you use the transfer pump method of emptying the tank (see under radiator entries), rather than unscrewing the radiator drain plug, replacing the sensor is a relatively quick job, once you have the tank out, and may be the first thing to try if you have a relatively newer/good tank (the new one is my third replacement - love those Ford/Jag plastics) and get the low coolant warning. Although, with the price of the complete new tank at less than $100, can't argue with that route either. Just noting that the sensors appear to be more short-lived than the tanks - at least the current crop.

 

I had gotten the msg. several times, only to find the level at/near the top of the tank. I ordered a new tank thru eBay. While waiting, I topped the tank and tightened the cap. I have not gotten the msg. since(4 months). Now I have a new, unused tank sitting with the rest of my new/almost new parts. I think I will just keep the new one as insurance against the msg. returning.