You are being a little sloppy with your terminology, and it is getting you into big trouble.
You did not measure S11 on your one port device. You measured the reflection coefficient. To measure "S11" you needed to start with a 2 port device, and to put a 50 ohm load on the unused port. Clearly, you just measured the reflection coefficient (which is load independent, as there is no port to add a load to).
Similarly, you can not convert a reflection coefficient into Z11, since such a Z matrix assumes a two port device again. Z11 would be the impedance of port 1 with port 2 set so I2=0.
What you CAN do is to convert reflection coefficient data on a 1 port into impedance data for that 1 port.
Assuming you did your measurement on a 50 ohm network analyzer, then the complex impedance of the device is:
Z = 50 * [(1+ρ)/(1-ρ)] where ρ is the reflection coefficient. (ρ is, of course, a complex number).