  Designing quantum systems with the measurement speed and accuracy needed for
quantum error correction using superconducting qubits requires iterative design
and test informed by accurate models and characterization tools. We introduce a
single protocol, with few prerequisite calibrations, which measures the
dispersive shift, resonator linewidth, and drive power used in the dispersive
readout of superconducting qubits. We find that the resonator linewidth is
poorly controlled with a factor of 2 between the maximum and minimum measured
values, and is likely to require focused attention in future quantum error
correction experiments. We also introduce a protocol for measuring the readout
system efficiency using the same power levels as are used in typical qubit
readout, and without the need to measure the qubit coherence. We routinely run
these protocols on chips with tens of qubits, driven by automation software
with little human interaction. Using the extracted system parameters, we find
that a model based on those parameters predicts the readout signal to noise
ratio to within 10% over a device with 54 qubits.
