I have used a Q meter for this. It resolves less than 0.1 pF. My GR 1658 bridge resolves much less but the readings aren't so reliable.
The problem is that the capacitance of the fixture is important. And simply putting the DUT into the fixture affects the strays. That is where the Q meter shines, in that you can watch the effect of position of the DUT and decide just what it is you want to measure. Also, it can measure over a very wide frequency range.
Some like to connect one end of the unknown, make a measurement, then connect the second lead and subtract the two readings. Not theoretically correct but still close enough for some purposes.
There are excellent papers written on this, many of them going back nearly a century. GR made some capacitance bridges. Later, HP did also.