I would like to use a 8753ES VNA to measure the module of the impedance Z of a LISN or in general of a DUT port.

With the VNA I can measure both S11mag and S11phase of the port. Then I can apply Z = 50 * (1+S11) / (1-S11), where S11 is complex.

From that formula I can get the module of the impedance Z but how can I get the uncertainty of the module of Z?

In a similar, the 8753ES (using the conversion menu) can provide directly the value of the module of Z but how can estimate its uncertainty?

The Agilent uncertainty calculator can provide the uncertainty of the two parameters S11mag and S11phase.

So, you have to do some work (and what you will find is that if the impedance is between 10 and 250 ohms, it's probably OK, but farther from that the uncertainty gets large). You need to compute a "circle of uncertainty" around your S11 impedance using max mag error and min mag error and max phase error and min phase error, from which you can find 4 S11 points. Convert these to impedance using the formula supplied and you will find the impedance uncertainty. For example, if you are 100,000 ohms resistance (S11=0.9048) then you can find S11 uncertanty (lets suppose it is 0.03), then the max and min will be .9078 and .9018; from that you can compute max and min impedance, which would be 1034 ohms and 968 ohms. This is for mag, then add in a phase offset and compute max and min (real will be about the same and but you will see an imaginary component).. Then convert the imaginary component to shunt C or series L by use Z=wL or Z=1/wC, etc, etc.