I was just perusing a list of state marriage laws here: http://www.theamm.org/marriage-laws
It looks like several states have fines or even jail time listed as punishments for breaking marriage laws. From what I can see the punishments are for people performing the ceremony who aren't allowed to do so, or otherwise engage in some kind of fraud. I have no idea if they come into play regarding the solemnization of an "illegal" marriage. I'll keep digging around as time permits. Unless I see a shiny object that captures my attention.