If you're lucky enough to own a monitor with direct hardware
calibration (basically, any NEC PA Series monitor, Eizo ColorEdge
monitor, or BenQ PG monitor), then you've enjoyed the benefits of easy
and high quality direct hardware calibration.
One thing not often mentioned with respect to this is the need to
calibrate these monitors multiple times in a row for the very best
results - especially with a new monitor, or with a monitor that has not
been calibrated for an extended period. If you calibrate on a tight
schedule, say every couple of weeks, this is not necessary, but if you
only calibrate now and again, it's well worth running through the
process multiple times in a row.
Calibrate multiple times with direct hardware calibration, for a more accurate result!
The reason this gives the best results is that the hardware
calibration systems spend a limited amount of time in the actual
calibration stage of the process when they're measuring and making
physical adjustments to the monitor's display. Because they want the
software to execute in a reasonable time, only a limited amount of
tweaking is done in any one calibration session. Sometimes there are
options in the preferences to increase the time this stage takes, it
depends on the system and the calibrator you're using.
The easy way to ensure that it spends plenty of time tweaking your
monitor is to simply run through the whole process twice, or indeed even
3 or 4 times. This will often result in significantly better
calibrations and lower deltaE numbers in the validation stage. Given the
whole thing is essentially automatic, it's well worth the trouble of
triggering it twice when you do sit down to do it.