In my opinion, from S-parameter S11,S21 we can calculate Z-parameter (or we can have directly Z-parameter).
We have the relationship between Z-parameter and C.
Z=1/jwC => C=-1/(w*im(Z)) where w is the frequency you want to measure
Download free SonnetLite, www.sonnetsoftware.com (I work for Sonnet). Bring up Sonnet, click on View Response, Browse for Project, change the file type (at the bottom) and load your S-parameter file. Then go to Output->Pi Model File. It will generate a lumped model based on your S-parameters. This will be a physical lumped model (if possible), not a lumped model based on curve fitting poles and zeros (for that select Broadband Model File, not available in the free version). To see if the physical model is valid, just see if the component values are essentially constant with frequency. There will probably be more than just a capacitor. If you get too many components (or no components at all), click on Model Options and you can set limits on component values.