Another word in praise of Armadillos. I have had one on my rear wheel for over a year. Only puncture I had was a thorn getting in thru' the sidewall. And yes indeed, they are almost run-flat (but not quite!).
However I have found thru' many years experience that the best puncture prodedure for me is to carry a spare tube that I KNOW is Ok. Then I can quickly bung that on, having checked the tyre for nasties, and repair the old tube at leisure.