I can explain the math of how VNA calibration works. I did it for my VNA project

http://www.github.com/profdc9/VNAUnder the "doc" directory there is a file called "VNA calibration method 2" you can read. It's brief, but explains the basic two port 6-parameter calibration that allows for a S11/S21 measurement.

A one-port measurement is especially easy and involves placing loads with three known impedances at the terminals in the fixture, usually a short, an open, and some resistance of a particular value, often the termination resistance of a transmission line, but it doesn't need to be that. The chicken-and-egg problem is to characterize your loads, which is why often the calibration standards are difficult to make.

The data that is measured is two complex-valued quantities, typically the voltage and current V/I at the actual VNA port, or equivalently the forward Vplus and reflected waves Vminus at the port since

Vplus = V - Z0 I

Vminus = V + Z0 I

where Z0 is the port's characteristic impedance, so if you know Vplus/Vminus you know V/I and vice-versa. For using an existing VNA port, Vplus and Vminus is convenient because S11=Vminus / Vplus.

The assumption is that the fixture is linear.. Therefore in general we can express the voltage Vembed and current Iembed at the embeded port as a linear function of the Vplus and Vminus voltages at the VNA port:

Vembed = A Vplus + B Vminus

Iembed = C Vplus + D Vminus

If we divide the first equation by the second equation, we get

Zembed = (A Vplus + B Vminus) / (C Vplus + B Vminus) = (A + B S11) / (C + D S11)

Because A,B,C,D can scale together, we set D=1 to fix a solution:

Zembed =(A + B S11) / (C + S11)

Now you place three known impedances Zembed at the fixture to be calibrated, and measure the S11 at the port of the VNA. Then you can get simultaneous equations for A, B, C.

Once you have A, B, C, you can measure S11 at the VNA port and calculate the impedance of the load at the embedded port.

And that is how you deembed one port.

Dan