I would have guessed that RFID tags would be less sensitive to dielectric constant. Can you explain why it's so sensitive at such a low frequency for an inefficient antenna (or is this a transmit antenna? which are larger).
If you have money, you can send it to Damaskos, they do an assortment of measurement techniques.
Resonator techniques are simplest. you make a transmission line with small cuts or breaks in the transmission line at spacing 1/4 lambda and another transmission line with cuts 3/4 lambda and measure S21. With accurate mechanical knowledge you have highest transmission at your proper wavelength. Since there is 1/2 lambda delta line length between the two samples, and the cuts are the same, you find the dielectric constant accurately. A coworker used this at my former workplace and got the answer that was higher than what Rogers corp. specified. I thought he was wrong until we made a microwave lens and proved he was right.
Rogers is now changing how they specify dielectric on many of their products from the "this is what we measured using a standard IPC measurement tehcnique" to "use this dielectric value for circuits"
kch