Colleagues of mine have done measurements with high-Q resonant structures and then use a VNA. The main downside is that you need a different structure for every frequency, and that the frequency will shift (slightly, if you know a rough estimate of the permittivity already) from design to practice.
If all you care about is the real value of the permittivity, measurements are 'easy'. Once you care about losses aswell, things become trickier. In resonant methods, you can use the Q to estimate the loss.
For higher-loss dielectrics, a through measurement with VNA can yield good results. The hardest thing is doing extremely low-loss dielectrics (PTFE, PE, Alumina, etc.). In this case, the loss component gets buried in the measurement uncertainty. I believe one method that can be used is to measure the real part of the permittivity with extreme precision (which can be done using mirror-based open-resonant cavity techniques) over a wide frequency range, and then use the Kramers-Kronig relations to extract the imaginary part. Spectroscopy people do this a lot (or at least so I am told).
On PCBs there is another interesting issue (rogers has a few good whitepapers on this) - the fact that most PCB materials, esp. those that have a glass weave, are actually anisotropic. As a result, depending on what type of transmission line/structure you are using, the permitivity is different. This is why in some Rogers datasheets the 'permittivity' and 'design permittivity' are different - one is measured by some standard IPC technique, the other is measured for a micro strip line.

You definitely spent a lot of time on the material research. The resonator method is too complex and time consuming for me

I personally prefer the transmission reflection method using VNA, because it is relatively easy to be performed and I usually work with low loss materials. The accuracy was acceptable for sub 1Ghz to 6Ghz applications. However, the differential length method still requires two microstrips. For simplify, I tried to do the measurement by using one microstrip and TDR. I even want to find out another method which can measure the Dk without the microstrip.

Yeah, the PCB is a troublemaker in both design and manufacturing. I was tripped by the manufacturing process control.
http://uniteng.com/index.php/2019/11/20/the-considerations-of-antenna-design-for-iot-and-wearable-devices/Page3, PCB :
The factors may affect PCB’s Dielectric Constant:
a. The Dielectric Constant can be dependent on the substrate thickness, the testing frequency, the operation temperature, the type of copper used and the microwave structure.
b. Two different microwave circuits using the exact same material will experience two different Dielectric Constant due to how the electromagnetic fields are using the different planes of the material.
c. Dielectric Constant was determined by a very specific test method which may or may not correlate to the microwave application of interest. The Dielectric Constant which is reported for a material can be dramatically different by the test methods.
d. The permittivity behavior is mainly attributed to dipolar moments and relaxation. Different dielectric materials will have different properties related to the dipole relaxation time.
e. The low-end material such as FR-4 may have worse dielectric tolerance, moisture absorption, passive intermodulation (PIM), Dk/Df over Frequency and Temperature etc.
f. In the manufacturing process control, the most of manufacturers in mainland China still used and only used legacy TDR equipment such as Polar CITS500s Controlled Impedance Test System. They may do not have capability to use the proper test method for the microwave application of interest.
g. In the manufacturing process control, the manufacturers usually do not follow the material’s datasheet. The impedance is controlled by achieving the different pressout thickness. They use copper thickness, copper area, resin, estimated dielectric constant etc. to estimate the desired thickness. The Prepreg's thickness may very under the different cure temperature and pressure. The Core’s thickness will not be changed during the laminating process.
