How to properly add dummy structures in HFSS

Many documents indicate that adaptive mesh in HFSS sometimes can not reach good solution.
A good treatment is to get understand the structure being simulated and wisely add some dummy structures to improve local meshing.

Can anyone tell me what material we should assign to dummy structures? Currently, I'm using air and choose length based inside soltion. Is it reasonale?
Currently, I can not get obvious improvements, though I have not tried finer mesh as computation power is limited.

I will be glad if someone will help or give any comments on this.