Cut it back

Here some more info.....

Here is a link that might be useful: clematis

It doesn't exactly sound like wilt - wilt begins at the top of the vine and progresses downward. And brown, dry leaves appear pretty late in the game. Generally, they will just appear limp and bruised looking. Brown or dry foliage, especially towards the base of the vine, is often associated with specific types of clematis and pruning issues or with excessive fertilization or watering/drainage issues. Clems need very good drainage in loose, organically rich soil that remains consistently moist. That is why one often reads the recommendation to keep their roots shaded or cool. It's not the shade that is of concern but rather the fact that soil exposed to hot, full sun conditions tends not to hold moisture evenly. Repeated drying and rewetting will cause the symptoms you describe. Keep the vine adequately watered and mulch well.

If it IS wilt (and I'm not convinced by the description), cut it back below the affected portion and tend as normal. Wilt is not contagious and has nothing to do with the soil. It is considered by most clematis authorities to be a failure of the vascular system of a not well-established clematis vine with an inadequate root system to support the considerable top growth. That is why it almost always shows up relatively early in the season when growth is most rampant and flowering is about to begin, why most clems suceptable to the problem tend to outgrow it (many, especially the species, are resistant) and why it is rarely, ever fatal.

If you can, post some photos on the Clematis forum and we can provide better advice.