An evergreen honeysuckle would be nice.

The one I have has fabulous scented flowers and flowers from June until very late autumn

http://www.flickr.com/photos/31559373@N00/4760266453/

I train an Euonymus shrub into a climbing plant they are very slow growing but mine now covers a 6ft trellis and has clematis going through it during the year. It has to be pruned back each year and grown with one or two stems going from the base.

One of my favourites is Hydrangea petiolaris . . . it is self-clinging (very low maintenance) has white flowers in June, and they still look pretty the rest of the year when they've "died" (see my photos).

You make it sound like your clematis doesn't have flowers in summer Mrspearson, you could plant several clems and choose them for their flowers so they're continuous through the year - including evergreen ones for winter flowers.

Sheilas suggestion of Hydrangea petiolaris is a good one because they're beautiful climbers (good in shade or semi shade too).