Conceitedness is the quality of being conceited — that too-high opinion of your own cleverness, looks, or skill, the kind other people disapprove of. It is a noun, so you can say “his conceitedness annoyed everyone.” Though actually, this is a stiff, bookish word. In real talk, people more often say conceit (“I can’t stand his conceit”) or they just call the person conceited. You will see conceitedness in essays and older writing more than in messages. Same frown as conceited: it is never praise.