Correct preposition for "competence"

I think "with" is the correct preposition in this case:

I have competence with computers/Our company has competence with programming and cooking.

However, I would like to add that "competence" is not usually used in this case, but rather "competent".

E.g.:

I am competent with computers

I'm going to partially agree with both answers. If you are talking about an abstract field of study or occupation (physics, computing, auto mechanics, and so on), you are competent in it.

I am competent in computing.

If you are talking about physical objects, you are competent with them:

I am competent with computers.

Searching Google books for competent with, I find

"competent with food, handwriting, and knowledge of bookkeeping," "competent with peers," "competent with the predicting strategy," "competent with people."

Searching Google books for competent in, I find

"competent in research," "competent in traditions of culture A," "competent in the practice of homeopathy," "competent in the domestic arena."

Most hits for competent in and competent with don't seem to fall in the scope of the OPs question, so just counting Google hits doesn't really tell you anything.