CPW based superconducting resonator using CST

I simulated some superconducting Resonator by CST. but I can't find any resonating in S21 by time domain solver, but when I used frequency domain solver, It resonated, but not in the right frequency. what is problem? I checked all the parameter I know, boundary condition, background material, accuracy etc.

If you think about the simulation method, high Q resonance and time domain solver is not a good combination.
The users that I know use Sonnet for accurate calculation of their superconducting resonators, and use CST only for visualization (field plots) of the superconducting resonators.

Thank you for your answer, I am trying to make some combination of CPW and Metamaterials structures, Sonnet seems to not good for metamaterials, and CST suit has enough solver to handle this situation, the problem is I just can not find a right good resonate in S21.

Good luck then. It's all about dense meshing and numerical precision.

I would first use the Eigenmode solver for the resonator alone without any coupling structure & ports. Once the desired resonance is established, you can proceed to a driven mode f-domain simulation.