Leaving a new or spent primer in there is not the way I do it. you can have as much as a half grain of water get past the flash hole and into the primer cup, not to mention the water that occupies the flash hole.
I use an old bar of glycerin soap, carve off a small fragment of it, then force it into an empty primer pocket and up into the flash hole so that it extrudes into the case body. Then I use a chop stick to knock the small extruded worm of soap off from inside the case.
This process ensures that only the internal case volume is measured and not the flash hole or primer pocket/cup voids.
From there, I place the case onto the scale and zero the scale. Then I use a syringe to fill the case with distilled water until the meniscus is just bulging out over the top of the case mouth, and record my weight. I do this on at least 5 cases in a given lot, and average the weight to get a value I use for that lot.
Also, you do NOT want to do this with a resized case. You do this with a fire formed case from the rifle you are going to shoot that round in, because that is the true volume of the case once ignition starts and expands the case walls into the chamber.
Once I am done taking measurements, I use the tip of my air nozzle and blow the soap out of the primer pocket so I can use the case, or if I have a large number of cases in that lot, I index that case by writing the measured volume in Sharpie on the outside, and place it in a loading tray I have set aside for measured cases, dummy rounds from a fresh barrel install or whatever. Makes it easy to go back and confirm later.