The Presidency of Maynooth was, in 1985 when Ledwith was appointed to the role, a senior position within the Catholic Church in Ireland. Only 44, he proved a capable administrator at Maynooth; immediately prior to his resignation he presided over the separation of the National University of Ireland, Maynooth and the Pontifical College. He was regarded within the church as a progressive and in 1988 he was seen as a series contender for the vacant see of Dublin following the sudden death of Archbishop Kevin McNamara. His name was submitted to Rome as one of three possible candidates.