ports and excitations in hfss

Even after reading a lot of material on the subject I'm still not really clear
on how to assign excitations and ports in hfss. I'd like to clear up my confusion by trying an "elementary" example : I'd like to calculate the
capacitance of a a parallel plate capacitor : two rectangular or circular
plates separated by distance d and with some material in the middle. The
geometry and material definition is straight forward and I have no trouble with that. I think I know how to setup an "airbox" around the system and
radiation boundaries... The main question is this : how do you define the
"ports" here?...I'd imagine this as a 2-port system which I can get S-parameters for; I can get capacitance from S-params which I can compare
against equations...

I think waveports is OK. And You can integrate voltage along one axial. You can try and make modifications.

waveports where? I have two plates, where do I put the waveports relative
to these plates? between them? also waveports are expected to be at the
edge of the system which doesn't seem as accurate as putting an air box
around the entire system and using internal ports

attached is an hfss script with the geometry and material definition
(no ports or solutions specified yet since this is where I'm stuck!)

You can try to place waveport on two opposite surfaces of the box which encloses the MIM cap, while lefting other surfaces being radiation boundary. Then to extract C12, C11 and C22 based on the simulated S-parameters.

are you sure this will work? there will be no connections between the cap
plates and the waveports; I always assumed that's necessary. Also from the
geometry, two of the faces of the cube will be "different" : these are the ones
parallel to the plates. The other 4 are perpendicular; you'd expect different
results if you picked the parallel ones vs the others.

Definitely you need connections between the cap plate and the waveport. You need to modify the cap a bit so as to make it suitable for simulating. The situation of connecting the cap plate to the waveport on the box edge is similar to edge-fed microstrip patch antenna.

The problem with this approach is that the connections between the plates
and the waveports at the airbox boundaries introduce new elements into the
system. Plus, the width and length of these connections,... are new variables.

The effects of connections can be de-embedded if u want the exact capacitance value.