Most any basic "good/bad" tester is simply a diode mode (emission) tester. They may also do grid leakage and shorts. You can test for a weak cathode by reducing heater voltage by one step, and more thoroughly test grid leakage (if so equipped) by increasing heater voltage by one step.
The really fancy ones (including the Hickoks that go for >$300?) perform these tests quantitatively (rather than qualitative good/bad), and also perform transconductance and perhaps other tests.
If you don't mind spending the time, you can also set up a breadboard to do the same. For transconductance, simply set up the device at the datasheet conditions, feed in a small AC grid voltage (maybe 0.1V), and see how much AC plate current comes out. The load resistance should be relatively small, a fraction of the plate resistance, to measure Gm directly without interference from plate resistance (which of course is more important for triodes than pentodes).
Tim