The assembled amplifiers are first tested at room temperature since it is a quick and easy way to check for major problems.
The first step is to check the transistor IV curves. The amplifier is plugged into the breakout box. Six power supplies provide bias for the three drains and three gates, and three ammeters measure the drain currents. It's probably best to measure the IV curves with the input and output of the amplifier terminated with 50 Ohms.
If the drain currents look reasonable, and can be controlled by the gate voltage, then take a full 2 port measurement on the network analyzer. I use the full frequency range of the analyzer to check for potential problems out of band. S11 and S22 will hopefully be well below 0 dB at all frequencies. Don't forget that the amplifier was designed to operate at 4 K, not room temperature. For example, the gain will increase dramatically as the device cools.
Disconnect the network analyzer, and look at the amplifier output on a spectrum analyzer while putting a variety of impedances at the input (such as short, open, and matched load) to help to check that the amp is unconditionally stable.
Assuming that at this point the amplifier still looks good, the noise should be measured. A short piece of stainless steel semi-rigid coax (about 10 cm) is connected to the input of the amp. The other end of this coax is terminated with 50 Ohms. The output of the amplifier is plugged into the calibrated noise test box. The spectrum is first recorded with the terminator at room temperature, then again with the terminator dipped in liquid nitrogen. Given the gain and noise of the test box as calculated from the calibration, and the hot and cold amplifier spectra, the gain and noise of the amplifier can easily be calculated.