Yes, there are standard capacitors. They are very expensive if you want them new. Used ones from General radio or HP are affortable and rather stable.
But it depends on your capacitance meters what you need. For some ebay special everything will work as long as it is within 1% or so. If you want to check a GR-1620 it will be a whole different story.
What meter, 3 or 4 terminal ?
What range, do you need pF or uF
Air capacitors are very stable, polyprop and mica too.
My oldest ones are air capacitors from Philips and from the 30's. They are still very accurate although the two terminal connection makes it useless for calibration. ( 100-1000 pF)
I have a HP decade that does 40pF to 1.1uF, that are mica and air caps. This is a three terminal and usable for normal LCR meters
For calibration I also have a GR standard capacitor that does 1 to 10 uF in steps of 1 uF. Has thee terminal connection.
But I have a GR1620 and I used that to make a collection of standard caps ranging 1pF to 100pF with 6 digit resolution, some nF values and some uF values. I measured them also on some calibrated good quality (non-Chinese) LCR meters. So these are good enough for calibrating or checking handheld LCR meters. Made them from PCB, used micas and some (not used) high quality ceramics I got from some one and were made for high precision RF circuits
http://www.pa4tim.nl/?p=3418 GR
http://www.pa4tim.nl/wp-content/uploads/2010/11/standaardcondensator.jpg one of the Philips