  Superconducting circuit testing and materials loss characterization requires
robust and reliable methods for the extraction of internal and coupling quality
factors of microwave resonators. A common method, imposed by limitations on the
device design or experimental configuration, is the single-port reflection
geometry, i.e. reflection-mode. However, impedance mismatches in cryogenic
systems must be accounted for through calibration of the measurement chain
while it is at low temperatures. In this paper, we demonstrate a data-based,
single-port calibration using commercial microwave standards and a vector
network analyzer (VNA) with samples at millikelvin temperature in a dilution
refrigerator, making this method useful for measurements of quantum phenomena.
Finally, we cross reference our data-based, single-port calibration and
reflection measurement with over-coupled 2D- and 3D-resonators against well
established two-port techniques corroborating the validity of our method.

Quantum Physics