In an older home with a two wire non grounded system.
Can a GFI be installed without being grounded to water system or some other means of grounding the outlet? I am unclear as the NEC make two specific notations about this type of system.
Thanks for the input.
Yes, but you must become the grounding conductor!
Care to give it a try?! 
No issue.
Two-wire systems are grounded, are safe, and are still code compliant. GFI’s will work.
However, it will not work with your standard 3 light tester (due to the way the tester works). Use the test button on the GFCI device itself to test.
If I am not mistaken, the only method that is authorized by the NEC to test the GFI is with the button on the device, anyway.
An ungrounded GFCI should be labeled as such. There is typically a label in the original packaging to use.
But how many devices have you found that test internally but fail to test externally or are wired wrong downstream and don’t test?
I don’t understand your point.
While I am not totally certain, I’m reasonably sure that the NEC recognizes the fact that some indications of “pass” or “fail” could be from faulty test equipment as well as faulty GFI’s. Accordingly, it officially allows and recognizes the test button on the receptacle, itself, as the test that counts.
My point is your point…
My question (or point) is that it can be as incorrect as any test device.
Does “as the test that counts” mean that it is the only acceptable test procedure that they recognize?
If so, I have dozens of cases where the device tested OK, but was not.
It came up in a recent thread, that sometimes when you press the test button, the GFCI will trip but not disable power to the receptacle.
It is my understanding that a GFCI can be wired to do exactly that. It will protect whatever is downstream, without disabling the power at the receptacle itself. If it should be disabling the power, then I write it up as “mis-wired”.
I’m not sure about NEC, but the test button is the manufacturer’s approved test method, which probably makes it the NEC approved method too.
I added the original comment to clarify for folks so they didn’t write ungrounded GFCI devices as defective because they did not trip with their three light tester. I do, however, use my three light tester to test the downstream protected outlets on grounded systems.
I always test GFCIs both ways and frequently find miswired downstream receptacles using the 3 wire tester. Actually, that is about the only way to test the downstrea, devices - no test button on them !