For any circuit, if you are going to characterize , you need to measure 2 parameters.
1. Quiescent current, 2. Full load current.
1=> Need no loading, and measure the total dc current and multiply it with the supply voltage. This will give you the Quiescent power consumption.
2=> Full load, (with load) you need to load targeted loading at the output node and then measure the supply current and multiply this with supply. It should give you total power consumption.
VCO generally loads to phase correction block and buffer.This all together may give capacitive loading in the range from 5p-10pF.So make assessment and add maximum output cap you expect.
Hope this will help you.