I have clematis Nelly Moser and Perle d'Azur in pots, but they aren't evergreen. Evergreen ones mostly flower in winter or very early. Clematis armandii is a good one. See others on this site. http://www.taylorsclematis.co.uk/clematis-evergreen-clematis/
I also have Trachelospermum Jasminoides (Star Jasmine) in a pot, which survived last winter -17° although the RHS says it is slightly tender. It lost a lot of leaves but they grew again and it did very well this summer. http://apps.rhs.org.uk/advicesearch/profile.aspx?pid=302
Lonicera Henryii is evergreen.