This is a bit messy, but you can do it with DIVs. As Sakin noted: I tried without success doing it in the stylesheet – but the following did work:
Insert something like <div style=”min-height:250px;”> on its own line before *every* widget content and a closing </div>, again on its own line, at the end. The “min-height” can be adjusted to suit the longest widget but not so big as to be silly! NB: This won’t work on a Twitter feed widget if you have one – but that is usually one of the longest anyhow. Doing this will allow you to keep your borders.