How to interpret the readings from tube tester?

A more pertinent question is how does one know the tube tester is accurate/calibrated?

As far as what is left in the tube, the Gm readings will give you a feel of the tube, not any with definite certainty of what's left in it. A good way to figure out how much life is left, the tube should be tested at a lower voltage. For example, test the 6SN7 at both 6 volts and 5 volts. If the Gm remains constant during the switch, the tube still has a good deal of life left. Some tube testers have a switch that reduces the voltage between 5% and 10% during a test - if the reading remains constant, it indicates a good tube; this way you don't have to worry about interpreting specific mho numbers - just the change (or lack of).

Again, what comes out of the amp can be totally independent of what is tested, and you cannot say with absolute confidence that a higher value tube will sound better or last longer than a lower one. It's a crapshoot, buying old tubes.

In additon to Ga5556's point "matching" is different for different circuits/amps. I just bought an old Citation to fool around with. Matching cathode currents, which is what most people mean isn't that important. You do not want them way off but you are looking for close Gm (transconductance).

I'm harldly an expert on all the different circuits and such but matching is not one thing and also a lot of tubes are matched in conditions that do not match how they are going to be used (voltages/currents) and so the "matching" tells you less than one would think and often they are tested/matched without proper warm up etc...

I remain,

RE: Calibration: Well, one knows it's calibrated from calibrating it (or having it done) from time to time. one of mine is easy to calibrate (Hickok 580), the other (TV-7) is more complex. But both are calibrated.

RE: Matching - agreed, the only way to really match is either with the tubes in the circuit in question (tricky for most users) or on a curve tracer, like the Tek 570. The 3 elements of matching (or at least 3 most common/crucial elements): Plate resistance (impedance), plate current, transconductance. Most testers only test one of the three. Some test 2. (current and transconductance). There's far more to it than can be written here, but suffice to say most of it is not really relavent in terms of getting good sound from tube gear. Microphonics (which are difficult to measure and only can be done in an audio circuit) are far more important in terms of what you hear.
-Ed