Verses with the word conceits in the New Testament (2 verses):

Romans 11:25
For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.

Romans 12:16
Be of the same mind one toward another. Mind not high things, but condescend to men of low estate. Be not wise in your own conceits.