I’ve been using the WordPress portfolio feature on my blog and website, but it turns out that portfolio tags are dealt with differently from post tags, as they are part of a custom content type with their own taxonomy. I searched around for the theme code to insert a tag list but the best I could find was this post (which obviously worked at some point), but a bit of database examination showed that the name of the taxonomy must have changed since this post was written, and they are now named jetpack-portfolio-tag (and jetpack-portfolio-type for the type).
Therefore the code to insert a list of WordPress portfolio tags into a theme is:
<?php the_terms(get_the_ID(), 'jetpack-portfolio-tag', $before, $separator, $after); ?>
using the optional $before, $separator and $after parameters to taste.