  We introduce an improved microwave calibration method for use in a cryogenic
environment, based on a traditional three-standard calibration, the
Thru-Reflect-Line (TRL) calibration. The modified calibration method takes
advantage of additional information from multiple measurements of an ensemble
of realizations of a superconducting resonator, as a new pseudo-Open standard,
to correct errors in the TRL calibration. We also demonstrate an experimental
realization of this in-situ broadband cryogenic calibration system utilizing
cryogenic switches. All calibration measurements are done in the same thermal
cycle as the measurement of the resonator (requiring only an additional 20
minutes), thus avoiding 4 additional thermal cycles for traditional TRL
calibration (which would require an additional 12 days). The experimental
measurements on a wave-chaotic microwave billiard verify that the new method
significantly improves the measured scattering matrix of a high-quality-factor
superconducting resonator.
