TDK has a couple of videos on this topic:
Interesting; the second video, "Measuring Capacitance accurately" shows a U1272A measuring a 100uF (93uF as measured with a precision bench LCR meter) MLCC as 66uF - approx 30% error despite having a spec of 1% + 2 digits.
This was attributed to the meter using too low a current for measuring larger, >10uF capacitors. The discrepancy, 30% versus 1% specification is enormous so what is going wrong? How could Keysight have got it so wrong, this isn't a $5 noname meter? Perhaps this error is specific to MLCCs, but that seems a far stretch. Something doesn't seem to add up here.
At 3:00 the EIA standard measuring condition for 100 uF capacitors is given as: apply .5 VAC at 120 Hz
At 4:00 the bench meter shows that the applied voltage is 499.926 mV (close enough to .5 VAC). To maintain that voltage across the 100 uF cap at 120 Hz requires a current of 35.1471 mA. Turning on the meter's ALC function reduces the driving impedance of the meter so that it can supply that much current.
When the ALC function of the meter was turned off at 4:35, the meter's output impedance reverted to the nominal 100 ohms, and at that impedance, the meter could only keep the voltage across the cap at 89.0973 mV with a current of 4.9 mA. That's what he meant when he said that the U1272A couldn't supply enough current (to maintain the voltage across the cap at .5 VAC). This is not the required standard condition used by capacitor manufacturers, so you don't get the capacitance specified by the manufacturer.
If a 100 uF capacitor of a type that doesn't have a large voltage coefficient, such as a film cap, were being measured, the voltage applied to the cap wouldn't matter; you would get the same capacitance for any applied voltage--the U1272A wouldn't have a problem.
The lesson is, if you're testing wonky ceramic caps, you have to use the same measurement conditions as the manufacturer if you want to get the manufacturer's specified capacitance. For large MLCCs, the U1272A (and probably most other hand-helds) can't do the job.