Hi, aa_talaat,
Here is a suggestion.
I would recommend that you connect the inductor from the center conductor of port 0 to the ground of port 0 with the shortest possible wires. If you could, I would recommend soldering it across an SMA female connector that directly connects to the location where you did the Open, Short, and Load calibration for S11. In your most recent pictures, with short cables, that would mean you use an SMA femaile connector and solder the part to the back of the SMA connector where you would normally mount it to the circuit board. As long as you connect to the same point as you did the open, short, and load calibration, the measurements should be pretty good. You can then measure the inductor directly by observing the S11 information.
Several of the programs (nanoVNASaver or nanoVNA_mod_v2 for example) will show you the equivalent parallel impedance of the device connected to port 0. What you should see on the Smith chart is a short at very low frequencies, say 50 kHz, (a dot near the left side of the Smith Chart) with an increasing impedance (primarily inductive reactance) of the device you have connected. On the Smith chart the plot should start near the left edge of the horizontal axis and proceed clockwise around the outer circle on the Smith chart as the frequency is increased. Based on what you have said, I wouldn't go much beyond 30-100 MHz as the stop frequency; however, experimenting with the stop frequency would be instructive regarding the device you are measuring. At some frequency, the inductor will appear as a very high impedance (this will be reflected by the plot going to the right side of the chart) because it will have a parallel resonance which is an indication of the amount of capacitance in your coil.
I hope this helps.
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Bryan, WA5VAH