This is something I've been thinking about recently as I don't currently showcase any of my UX work, only front-end web development which is much easier to deal with.
The problem I've encountered is that all my UX stuff is part of a process, and not really part of the public-facing finished product, so clients have generally been very unwilling to give me permission to display any of it, as it's not really public-domain material, and in some instances partly gives away how the agency or company that I'm contracted to works.
What I've resolved to do is show obfuscated (i.e. "de-branded") wireframes and screen shots of prototypes that show the process I work through, but not to show any of the related finished products to maintain client anonymity. This shows prospective clients that I know what I'm talking about, and I know how to use my tools. The best approach I've seen for displaying UX stuff is a little intro to the project with and outline of the brief, a short walk through your approach/process/logic and of course a few screenshot - no need to mention client name (unless approved o course).
I'm currently in the middle of redoing my own portfolio site which will contain UX stuff displayed as outlined above, along with my more "traditional" web development stuff. I'll be building a fairly standard-issue WordPress portfolio site to display the lot, which is a fairly easy way to do it althogh there are a ton of other CMSs/sites out there tat will work just as well.