If you don't have a nearby dealer with a tube tester, it might be nice to have one of your own. Most of the currently available models test only the most commonly used tubes (particularly tubes used by musicians in guitar amps). My local dealer uses several vintage TV-7 testers and the modern Orange tester. I like the Orange because it is simple to use (you don't have to look up tube data to set the numerous dials and switches that have to be set on the TV-7), and it is pretty stringent in its rating. Tubes that test quite good on the TV-7 often fail on the Orange and the Orange tends to be correct that the tube is failing.
I have an Amplitrex, which is a tester in a different league. It tests at full power so it sort of stress tests a tube, it is simple to use (idiot-proof is a must for me), and it tests a lot of different parameters. If you hook it up to a laptop, it will even curve trace the tube. The big downside is that it is expensive.
The alternative to testing is to have back up tubes that you know are good and fresh. If you swap these in and the sound is dramatically different, you know that at least some of the tubes in your currently operating set are becoming weak. You can then do one-by-one swapping to perhaps identify the culprit; alternatively, you can just change all of the tubes at once and get a new set of reserve tubes.