Hi R@SE,
I use lumped elements inside my eigenmode solver all the time, there should be no problem in simulation.
Measuring the dispersion of an antenna would be an interesting thing to do; I feel like jiripolivka may be able to provide more insight into this, as I have no idea where to begin.
Edit: Are you familiar with effective medium parameter retrieval? As far as I know, this requires a two-port network, but perhaps someone has developed a way to obtain such parameters for a dispersion diagram using only one?
Good Luck