In CST, very easily modes can be found out and figured out, but in HFSS, you can find out modes after setting your ports using Eigen mode solver. But, here, it will not be written TE or TM mode. So, you have to analyzed first TE and TM mode and then proceed for mode index by checking your field profiles.
The eigenmode solver calculates the cavity modes (TE and TM modes). If a similar structure has been analyzed using CMA, probably you can make analogy between the two.
Probably I am not on a good terms with CMA theory, but every time I try a metal-dielectric-metal tablet, Eigenmode in HFSS gives me all the correct and expected modes, and CMA tells that no significant modes are found.