I am probably going to make a fool of myself here, but I'll take a
guess that the nanoVNA only uses the OSL for S11 calibration and isolation/through for S21, and that the calibration will normalize the S21 logmag to 0dB and phase to 0° if you had a through fixture of the same design/geometry as the matching network board. If I am wrong, at least this topic is getting a bump lol.
Not sure what nano you have, but mine will not show the S21 shunt impedance values directly. The best mine can do is show the polar values or the logmag in dB and the phase angle. So, what I ended up doing while trying this is setting mine to display S21 polar values and punch that complex value into a formula for the shunt through device impedance. But I think in your case, you would do that math backwards and calculate the expected polar values from the impedance you need to match so you can watch for that while adjusting. For example, I am fairly sure that 5-5i would translate to a S21 polar plot at 0.19-0.14i on my nanoVNA.
Edit: Table 1 of the article linked below shows the formulas for converting between polar s-parameters and the device impedance. The only issue is that where you see Zdut, Zref and S11 or S21, those are all complex numbers and doing that math without a calculator that does complex math (like a TI-89, a phone app like HyperCalc, or even MS Excel), it gets a bit messy.
https://www.edn.com/accurately-measure-ceramic-capacitors-by-extending-vna-range/Edit 2: I have read that shunt-through measurements are very susceptible to common-mode currents. That means sheilding or baluns if you want to get serious. My nano does fine with S11 until it gets below about 2Ω, so depending on your situation and your nano, it may be easier to trust the S11 reading.