While having a chamber gauge as sold by Brownells or Parker Hale is a good option I have discovered they are not failsafe because different manufacturers have different standards for how they cut the chamber.
I have noticed that my German made guns have slightly tighter (smaller) chambers than my Belgium and Brit guns and the Brownells 16ga does not fit my German Gun marked 16/70mm 2 3/4in. So a chamber gauge that works perfectly in a modern Browning Citori 16, 1920's Greener 16, 1920's Belgian 16, may not tell the full story and you need to measure as 2-piper has described.
That said numerous traffic has been posted on shooting 2 3/4 in 2 1/2 guns with immunity. As a general rule I try to do what the manufacturer intended and believe you should too.
