As previously mentioned, the problem is because of the lack of a 'ground plane' or return circuit to the nanovna (or HT).
Search the web for "tiger tail" or "rat tail" and ht or handheld radio. There are many results about adding a 1/4 wave counterpoise wire to the HT. Some have measured and posted the results of tests, which were quite good.
QRP "walkabout" or pedestrian mobile HF operators often use what they call a "drag wire" counterpoise, which trails along behind them on the ground.
I made one for my UV5R HT, using some #28 silicone covered, very flexible wire that is also quite limp. It seems to have helped a lot. I intend to operate battery portable, and bought this BNTECHGO brand wire from Amazon for making small, lightweight counterpoises and maybe (shorter) antenna wires.
At first, after reading about the 'tiger tail' counterpoise, I tried a leftover piece of very thin magnet wire, but it was too stiff and inconvenient. The limp silicone wire is much better, although a little bulkier (but still tiny).
To connect it to the HT, I stripped the end for about 3/4 inch and bent it into a circle. Then adjusted the circle diameter to fit easily over the threaded antenna connector on the top of my HT. After soldering the little loop, i place it over the threaded SMA post on the radio, then screw on the antenna. That clamps the counterpoise wire in place. That last bit, with the antenna base being wider than an SMA cable connector, would be the difficulty with this method with the nanovna.
A simple way would be to connect a 1/4 wave wire to an alligator clip, and attach the clip to the SMA connector shell. I've done this, both for a multiband HT antenna, and for a mobile antenna. It works. (Moving the counterpoise will still affect the nanovna readings, but much less.) Hand position will not have such a large effect, either.
And it's cheap and easy to try!
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Doug, K8RFT