For model dependency , I recommand you read the k-k ralation concept(http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relation ). I think you can get the answer.
BTW, Hyperlynx support casual wideband Debye model(Setup-Preferences, check on "Use Advanced lossy-line mode").
The requirement at low frequency is that the imaginary part approaches zero and that the derivative of the real part approaches zero. This is because at DC (0 Hz) the reactance is zero. The real part needs to cross 0 Hz horizontally so that the impedance curves is continuous as it passes into the theoretical negative frequency region.
At the high frequencies, I don't think we can characterize every possible resonance. The main reason for the requirement derivative of the S-parameters approaches zero is so that the complex pole fitting algorithm can do a good fit. If the high-frequency data is rising or falling dramatically at the end, then a simple extrapolation to higher frequencies, that may be needed for a simulation, would probably make a non-passive model. The complex pole fitter enforces the flat response at the highest frequency, so if the data is not approaching flat, then the complex pole fitter has to invent some data to get the flat response at the high end.
As I recall, the even and odd function behavior is related to the Kramers-Kronig relation.