We report measurements and uncertainty analysis on a cryogenic low-noise amplifier (LNA) with a very low noise temperature (NT), among the lowest noise performances reported at microwave frequencies. The LNA consists of three stages of InP high electron mobility transistors with a gate length of 130 nm. It exhibits about 44 dB gain and less than 2 K average NT in the operational band of 4 GHz to 8 GHz. A detailed uncertainty analysis is outlined to evaluate a variety of error sources in the measurement. The calculated uncertainty shows as low as 0.1 dB on the measured gain of about 44 dB and 0.18 K on the measured NT of 1.65 K, indicating excellent measurement accuracy. A breakdown of the uncertainty components helps identify the major causes of the overall uncertainty and enlightens us about how to further improve accuracy. It is important to know the actual physical temperature of the passive termination that is used as a cryogenic noise source in experiments. Due to its large temperature gradients, the commercial matched load is replaced by a custom-made attenuator that is isothermal and consequently provides reliable NT measurements of the LNA. The precision measurement technique developed at the National Institute of Standards and Technology is independent from the manufacturers' characterization method. This study marks the first time that such a low NT from a cryogenic LNA is verified independently with such a low uncertainty.