Every inspection is an estimation... there are no perfect gages!
The jaws of the chuck that you use to check runout with are never exactly coaxial with the axis of the spindle bearing that the chuck spins on.
The bearings themselves always have error... but most of all no one can ever inspect the infinite set of circular cross-sections perpendicular to the axis to reveal the one with the greatest measure of runout error.
Does this mean that no one method can be labeled "best" or "most accurate"? you bet!
So can one estimate circular runout on a CMM? Of course they can! The quality of the estimation depends upon the accuracy and precision of the tool and the skill of the operator using it.
DCC CMM's are typically easier to use to accomplish the analysis because the software can drive the probe tip to touch (or continuously scan) the surface of revolution perpendicular to the resolved datum axis orientation no matter what its rotation from the machine's axis is. With a manual CMM one has to set up the datum feature(s) axis reasonably perpendicular to the machine's axis to get the best estimation of the circular cross-section's runout.
For both types of CMM each point is figured for its radial displacement to the established datum feature(s) axis and the difference of the MAX and MIN values can be reported for circular runout. Naturally a reasonable number of individual cross-sections would be examined according to the expected or observed variability in the cross-section results. If one wanted to estimate the total runout the MAX and MIN radius values of all cross-sections sampled would provide the total runout.
Sometimes when there is an accurate spindle, with an equivalently accurate chuck and a sufficiently long and stable registry of the datum feature that may be the best tool to use for the inspection and sometimes other tools or even a CMM is better suited to perform the inspection.
Paul