I am setting up a lab involving a parallel plate capacitor connected to a 6V source and an electrometer. After disconnecting the voltage source from the capacitor, I attempt to find the charge stored in the plates by dividing the voltage of the capacitor by the distance between the plates. However, my electrometer reading of voltage is heavily altered by where I am standing. Is there any way I can make sure the electrometer reading is correct?
Good news: the reading is correct!
Bad news: you cannot really change the electromagnetic properties of your body significantly (aside from rather unpleasant methods such as freeze-drying), so you'll have to live with that fact.
Recommendation: 6V is very little voltage, so the charge on a plate capacitor (which is very low-capacitance for plates that are not just a few micrometers apart) is very low, and thus minor changes of electrical field due to (charged) bodies nearby make a relatively large impact.
You could try to ground yourself and one plate (i.e. connect to one of the two plates, and that to a common earth, that you also measure against), to at least try and minimize charges having their own potential that might be much much higher than.
Alternatively, if you can, use a much higher voltage. Since everything in electrostatics is linear (until materials aren't, but that's not the regime you're working in), the external effects don't reduce – they just become less important. The dielectric strength of (dry) air is some 3·10⁶ V/m, so if your plate gap is at least 100 µm, you can apply 300 V to the plates. Since you don't want things to be dangerous, and since you probably don't control the humidity of air in the gap, back of by a factor of ten, and start with 30 V for your minimum gap width.
Of course, but I guess you're doing that already, move your measurement equipment away from where you're standing, and maximize your distance to the plate capacitor.