Accurately measure high quality factor coils
I know two papers in the academic literature (IEEE) regarding measurement of Q factors in your frequency range, maybe they can help you. Both use mica or porcelain capacitors in the resonance circuit to obtain the lowest possible capacitor ESR.


Zulauf and Rivas-Davila, Single-Turn Air-Core coils for High-Frequency Inductive Wireless Power Transfer


The first one uses a VNA (E5061B) to measure the impedance magnitude of a resonance tank consisting of the inductor and a parallel capacitor. The impedance is measured around the resonance frequency and then they use the 3-dB method to find Q of the resonance tank, \$ Q_T \$

\begin{align}
Q_T = \frac{\omega}{\Delta \omega_{3dB}}
\end{align}

Then the quality factor of the coil is back-calculated

\begin{align}
Q_L = \frac{Q_C Q_T}{Q_C - Q_T}
\end{align}

For reference, they report errors of 1-4 mohm between simulation and measurement resulting in loss of up to 100 points in quality for the experimental setup. 


Han et al., Evaluation of Magnetic Materials for Very High Frequency Power Applications


In the second paper, a RF power amplifier feeds a sinusoidal current into a series resonance of the inductor and a capacitor: ground -> amplfier -> L -> C -> ground. The input (ground to amplifier output) and the output (voltage over capacitor) are measured using ground referenced oscilloscope probes. The peak ratio is found manually by tuning the frequency and then calculating the quality factor:

\begin{align}
Q_L \approx \frac{V_{out}}{V_{in}}
\end{align}

However, \$Q_C\$ must be much larger than \$Q_L\$ to have good accuracy and this will be difficult in your case.