For an equivalent circuit, analyze the coupled line in SonnetLite (free download
www.sonnetsoftware.com, I work for Sonnet) with ports 1 and 2 on one side, ports 3 and 4 on the other, both numbered from top down. Set reference planes so you have one or two cell long transmission line (i.e., very short length). Make sure the total line length is at least twice the substrate thickness. After you get S-parameters, display a graph of the data.
Now, with the graph displayed, go to the Output menu (at the top). One of the options is to output R, L, C, and G parameters of a coupled line. These are per unit length, where the unit length is the de-embedded length of transmission line you analyzed. This model can be used in various versions of SPICE. There will be one model for each frequency you analyzed. Check validity of the model by making sure the models change very little from one frequency to the next
You could also do this in Momentum and export S-parameters. Then load them into the Sonnet graphing program and again go to the Ouptut menu. However, customers comment that when they do this with Momentum data, the model varies a lot with frequency and the problem appears to be due to small errors introduced by their de-embedding. (This sort of model extraction is very sensitive to small errors.) My guess is that it is because without a perfectly conducting sidewall, they do not have an exact ground reference for the ports. Several unsuccessful attempts have been made by these customers to get full technical details of the Momentum de-embedding. If anyone knows where Momentum de-embedding might have published details, please let me know. (Sonnet de-embedding was completely detailed many years ago, but also in the most recent MTT Trans.)
To get odd mode, in Sonnet make the input ports 1 and -1, output ports 2, +2. For even mode, make both input ports 1, and both output ports 2. Even and odd mode impedances come directly out of the Sonnet de-embedding, or you can take the RLCG model and use Z = sqrt( (r+jwL)/(g+jwC) )...this works fine unless you don't happen to believe in complex Zo (in this case, please see your minister). Also, this will be off by a factor of 2, don't remember which way, but it is in the manual included with SonnetLite.