I found a couple of capacitors, one of ordinary loss, and the other is low loss.
Those measured values I'm relying on to be accurate were made on a Hioki IM3570.
Capacitor A has a D value of .00135 at 1 kHz, and a D value of .0025 at 10 kHz.
Capacitor B has a D value of .000184 at 1 kHz, and a D value of .000256 at 10 kHz.
Capacitor A was chosen because its D value of .00135 is slightly larger than .001, which is where the low performance (cost) meters will begin to have trouble getting a good measurement. What I mean by "have trouble" is that the measurement of secondary parameters D, ESR, Q will be incorrect or noisy (fluctuations in the measurement digits).
I would expect that low performance meters will be able make reasonably accurate measurements of Capacitor A, but they will get bogus results for capacitor B, whose D value of .000184 is substantially less that the threshold of .001
Here are some measurements of these two capacitors made with a high performance meter (Hioki IM3570), and a popular low cost meter (DE5000):
Hioki IM3570 DE5000
@1kHz @10kHz @1kHz @10kHz
C 10.435 10.409 10.446 10.419
ESR 20.4 3.90 19.3 3.51
Capacitor A D .00135 .0025 .001 .002
Q 735 393 785 434
Hioki IM3570 DE5000
@1kHz @10kHz @1kHz @10kHz
C 10.268 10.267 10.269 10.274
ESR 2.84 .396 1.03 .16
Capacitor B D .000184 .000256 .000 .000
Q 5450 3920 OL OL
Capacitor A has a 1 kHz value of D of .00135, which is somewhat larger than the threshold value of .001, and we see that the values measured by the DE5000 are quite comparable to those obtained by the Hioki.
Capacitor B has a 1 kHz D value of .000184, which is quite a lot smaller than the threshold; we should expect that the values obtained by the low performance DE5000 would be considerably in error, which they are.
These experimental values show that low loss capacitors can't be correctly measured by low performance (low cost) meters. The user should always measure D or Q as well as ESR. If the D or Q values are beyond the threshold values of D<.001 or Q>1000, expect that the measurements will be substantially in error. IF the capacitor being measured is very low loss, low performance meters may not be able to make any measurement at all, or will return totally bogus results.
Even if the value of D is not checked, the fact that the ESR value is unstable means that the capacitor being measured is very low loss, and if the meter is a low performance unit, the measurements may be wrong. The front end noise of the meter is contaminating the measurement. You just can't correctly measure secondary parameters of a very low loss capacitor with a low performance meter, although the capacitance measurement will be good.