Pierre,
I think you are trying to measure the antenna from a handheld transceiver?
In such instances, the antenna uses the handheld transceiver as a ground plane to make up the other half of the antenna. Without the antenna attached to some tye of adequate ground plane, the SWR will be greatly affected by anything in close proximity. The antenna will use the nanoVNA test leads and nanoVNA itself as the other half of the antenna. Even your hand touching the nanoVNA or test leads become part of the antenna.
I suggest using a magnet mount attached to a metal ground plane as a "testing jig".
