I am trying to plot the dispersion diagram for a transmission line metamaterial IFA antenna, consisting of a capacitor in series and an inductor in parallel to the antenna.
As far as I know, the dispersion diagram is the plot of frequency vs. phase of S21, as phase (theta) is beta*length.
But how to plot the dispersion diagram of an antenna which has only one port?
You're correct that dispersion details the phase propagation of a given mode versus frequency -- so you obviously cannot obtain this information from the input parameters of an antenna.
What you can do is simulate the metamaterial structure on its own, and obtain the dispersion from that.