If anyone does read the paper linked to by Roger the test setup for s11 in that paper is shown in figure 4 and it is awful with bits of wobbly copper tape and a metal bar making up the short and the open. They claim they try and correct for it using equations based on a crude circuit model for their unsuitable test jig. I don't think they know what they are doing. It appears that they don't actually realise that their de-embedding won't account for the uncontrolled nature of the short and open system they are using. The damage (to the measurement uncertainty of mag r of the test cap) will already have been done during the SOL calibration. You can get away with a crude system like that if you just want to measure the capacitance of the component but if you want to measure both the magnitude and angle of the reflection coefficient of the capacitor you need to have extremely well defined open and short circuit connections.
To make the measurements I'm making I use a GHz rated text fixture where the fixture/cal Zo is very well controlled right up until it hits the open or the short discontinuity at the end of the cal kit. I'm using a cal kit where I should have the offset delays for OPEN and SHORT corrected to (hopefully) less than 1ps. I'm using a precision 50 ohm load for the cal kit. This might seem over the top but the offset delays for the cal kit need to be known quite accurately or errors can creep in for critical measurements like this.
It appears that they are measuring just under 0.2R ESR for the 1nF cap across VHF using s11 That is a Q in the ballpark of just 20! They get 0.05R ESR using another method. I'm not surprised they are getting strange results with s11 (like a Q of 20) because their test setup is an uncertain mess.
