The plasmid DNA minipreps didn't contain any plasmid at all (except for the positive control that I'd seeded with a known amount of plasmid). But this might just be because my frozen competent cells were old and not very competent at all. Their transformation frequency was only about 2.5 x 10^-4, so even if the competent cells had taken up supercoiled plasmid I probably wouldn't have been able to detect it in my minipreps.
I may repeat the experiment one time, using fresh competent wildtype and rec-2 cells. (The rec-2 mutant cells can't transport DNA out of the periplasm, so may give higher sensitivity.) Or I may decide that this experiment shouldn't be high on my priority list because it isn't something the reviewers of our previous proposal were concerned about.