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By connecting the other meter probe to the other side of the capacitance (wherever that is). This is exactly the same scenario as the capacitor would see in real life, the charge is built up against some or all surrounding objects. You need to identify them and either use or simulate the same conditions.
Assuming this is is the cap on top of a Tesla transformer, a better method is to measure the resonant frequency of the coil with the sphere capacitor attached, then remove it and replace it with a fixed capacitor (~100pF). From the difference in resonant frequencies you can calculate the original capacitor value. Obviously, do this with the power turned off!
Its a single conductor with capacitance and it apparently is only computed not measured with an LCR meter rather with some form of electrostatic meter which shows how much force it exerts.
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