RadioRon is of course correct that time is the physical property we can measure most accurately. Here is a quote from an article in Scientific American, September, 2002:
"The primary time standard for the U.S., a cesium fountain clock installed in 1999 by the National Institute of Standards and Technology (NIST) at its Boulder, Colo., laboratory, is good to one part in 1015 (usually written simply as 10-15). [edit]...space-based clocks set to fly on the International Space Station by 2005 are expected to tick with uncertainties better than 10-16. And successful prototypes of new clock designs--devices that extract time from calcium atoms or mercury ions instead of cesium--lead physicists to expect that within three years, accuracy will reach the 10-18 range, a 1,000-fold improvement in less than a decade."
Oh, how I love exponents! One part in !0E-18 is less than one second from the beginning of the Universe.
I did not download the whole article, but as I recall from when I read it in 2002, the author from NIST made a comment that they could tell on which floor of the building they were by the relativistic effects of gravity on time.
Now, there are easier and far cheaper ways to tell on which floor of a building one is standing. Which gets back to the OP's question of measuring capacitance. Despite the accuracy of time measurement that is readily available, can the other variables be controlled (with reasonable cost) to attain the accuracy needed for the capacitance measurement requested?
That is meant as a question, not a criticism, because I really don't know the answer. However, just thinking of a few of the factors that can lead to changes in capacitance, makes me think that Nigel's comment about being an ambitious is goal right on. John