Google gives 4½ hits:
http://www.google.com/search?hl=en&q=contumulate&btnG=Google+Search

I had to look up contumely again (Gurunet):
con·tu·me·ly (kŏn'tû-mə-lç, -tyû-, -təm-lç)
n., pl. -lies.
1. Rudeness or contempt arising from arrogance; insolence.
2. An insolent or arrogant remark or act.
[Middle English contumelie, from Old French, from Latin contumçlia; akin to contumâx, insolent.]
How odd--a noun that ends in -ly. Just think of saying, "My newest employee gave me a contumely."