The Coat of Arms of Montserrat was part of a grant of composite Arms given to the British colony of the Leeward Islands in 1909. The flag of Montserrat is simply the Montserrat arms placed on the fly of the British Blue Ensign and was taken into use sometime considerably after 1909, quite possibly after the colony of the Leeward Islands (which consisted of several British-administered islands in the region) dissolved in 1958, making Montserrat a stand-alone colony.
The Governor of Montserrat maintains a separate flag. The Governor's flag consists of a Union Flag defaced with the coat of arms. This was introduced after the dissolution of the Leeward Islands in 1958, when Montserrat became a separate colonial entity.