I could add a few things to this topic. A VNA makes measurements in a 50 ohm (or 75 ohm) environment. It is expected that the connection between the ports and the Device Under Test (DUT) is a 50 ohm characteristic impedance coaxial interface. (Let's not get into waveguide at this time). Calibration is performed at the end of the coaxial cable by various means but always using standards which are well known and characterized so the VNA knows what the measurement of each piece should be. It is pretty much impossible to create open, short and load calibration standards that will work with alligator clips unless the frequency is limited to 10 MHz or so.
To be really clear, if you calibrate to the ends of a pair of test cables and then attach a short "Pigtail" coax with the other end stripped to expose 0.1" of center conductor, you can use port extensions to fix the phase and delay error and move the calibration plane to the end of the pigtail. All well and good so far, but that 0.1" of exposed conductor is no longer surrounded by it's coaxial ground and is now an inductor equal to about 22 nH per inch. In this case, 2.2 nH for 0.1" of exposed conductor and another 0.1" to get back to the ground shield for a total of 4.4 nH. That will have a reactance of 50 ohms at 1.8 GHz, so that is the bandwidth of the measurement capability of the cable and pigtail arrangement.
When I designed fixtures, I had an SMA connector which attached directly to a "Pogo pin" which itself was contained within a coaxial hole in a brass fixture. The ground surrounding the pogo pin was spaced to create a 50 ohm characteristic impedance WRT the pogo pin. The pin itself protruded from the opening somewhat but was compressed flush with the opening when pressed against the DUT interface. This maintained 50 ohms all the way to the DUT. It was then possible to calibrate to the ends of the test cables and use port extensions to the DUT interface by measuring a short in the fixture and adjusting the port extension delay until 180 degrees is seen in the S11 and S22 phase measurements.
Hope this is helpful.
Best,
Brian