Captain of Engineering is the title given to chief engineers who hold the rank of captain.
In 2285, Montgomery Scott was ordered to report to the new transwarp vessel, the USS Excelsior as the captain of engineering. (Star Trek III: The Search for Spock)
He may have kept that title aboard the USS Enterprise-A, however, he was described as the "chief engineer" by Kirk in Star Trek VI: The Undiscovered Country.
Geordi La Forge was given this title in the novel Indistinguishable from Magic after being promoted to the rank of captain, but later returns to being a Commander by the time of Plagues of Night.