There are two different and basic solutions here depending on the type of copy being written.
Copy tied to a specific design
If the copy is tied to a certain layout or is a one-off page, advertisement, or other piece of limited "lifetime" of availability then you probably want to capture a screenshot of the site and post thumbnails. The thumbnails could then open up a larger image/PDF version of the work. If you can tie in some visual to break up the listing of text on your site that's great, but not necessary with a copywriter's portfolio I would say.
Copy not tied to a specific design
If the copy is more like written articles for a newspaper, or anything lengthier it probably can be considered detached from the original design and artwork. In this case you could link to the actual content using an inline text link. Presumably the viewer of your profile is going to be taking a close look at how you write the content on your portfolio as well as on the sample site/article/post so you should feel comfortable just using text. In theory you could still post a clickable thumbnail which would open up the site in a new window or a frame. The frame keeps the viewer on your site, but you run the risk of certain sites not playing well in a frame. I think this is something you'd need to evaluate on a case by case basis -- but keep the behavior consistent on the individual portfolio.
There is a problem common to both of these types of copy, in that the target sites may move or change. You'll need to stay up to date with your screenshots and descriptive copy on your portfolio in order to ensure there's no mismatching, out of date links, or out of date thumbnails.