Máel Muire Ó Connaig, Bishop of Kilmacduagh, died 1224.
Máel Muire Ó Connaig may have been the first of a number of a number of members of the same family who occupied the see. Énri Ó Connmhaigh (fl. 1405) and Seaán Ó Connmhaigh (1441–78) may bear later forms of a surname that is now rendered as Conway.
Bishop Ó Connaig predecessor, Ua Cellaig, died sometime in 1215 but it is not known when he himself was appointed or consecrated. He died in 1224.