The coat of arms of a diocesan bishop is composed of the seal of his diocese and his personal arms, adopted when he became a bishop. 

Bishop McHugh’s personal arms, located on the sinister impalement of the coat of arms (on the right of the viewer) were adopted at the time of his election to be Auxiliary Bishop of Newark, New Jersey. Bishop  McHugh has employed a design that brings together those elements of his priestly service that have had the most significance in his life. The design is based on the symbol of the dove, overshadowing five small circles on a blue background. The dove represents the Holy Spirit and the five small circles represent the cells of life and family units. The model of the dove is taken from the pulpit of the Cathedral of the Sacred Heart in Newark. This symbol represents the Bishop’s pastoral work in the family life and pro-life movements in the Archdiocese of Newark and at the national and international levels.

Coming forth from the bottom of the impalement are three gold, rugged mountains, representing the mountains of the Potenza region of Italy and honoring the Italian heritage of his mother, Caroline Scavone McHugh. On these mountains is a green trefoil (shamrock) taken from the McHugh family arms and honoring the Irish heritage of the Bishop’s father, James Thomas McHugh. Above the dove is a silver crescent, from the device of the Archdiocese of Newark. The crescent is flanked on one side by a silver fleur-de-lis to honor the former Archbishops of Newark, Thomas Boland and Peter Gerety, as well as to signify the Dominican Order, which operates the Pontifical University of St. Thomas Aquinas, Rome, from which the Bishop received his doctorate in Sacred Theology. On the other side, is a silver ermine spot, taken from the arms of Archbishop Theodore E. McCarrick, whom Bishop McHugh served as an Auxiliary Bishop in Newark and who himself had taken the charge from the arms of the late Terence Cardinal Cooke, with whom Bishop McHugh also worked for many years. 

For his motto, Bishop McHugh selected the Latin phrase, “Quid retribuam Domino” from Psalm 116:12, which means, “What shall I return to the Lord.” In this phrase, Bishop McHugh expressed his goal in life, to return to the Lord all that he can for all that he has been given by God, through His Son, Jesus Christ. 

The arms of the Diocese of Rockville Centre, located on the dexter impalement of the coat of arms (on the left of the viewer), are based on the history of Long Island and the etymology of the name Rockville Centre. The shield is divided per saltire and is bordered by a bordure composed of wavy lines. The colors of the field within the bordure are gold and blue. These identical colors appears on the coat of arms of King William III of the House of Nassau and on the arms which the county of Suffolk in England has used at times, these arms being those of Ipswich.  

Three of the four partitions formed by the saltire are emblazoned with a scallop shell. Although there are more than 12 names for Long Island, the name generally preferred by the Indians of the mainland was Seawanhacky or “Island of Shells.” The scallop shell is also truly heraldic, and a symbol which is often used to signify the flowing of water in the Sacrament of Baptism. 

The wavy silver bordure is the heraldic equivalent of water and surrounding, as it does, the other charges, signifies the insular nature of the diocese. The lamb’s head is the symbol of St. Agnes, virgin and martyr, the titular of the Cathedral of the Diocese of Rockville Centre. St. Agnes has been represented with a lamb, the symbol of her virginal innocence, since the Middle Ages.  

The black roundel in the center of the shield with the three stones or rocks affords canting arms for Rockville Centre. The black roundel is in the exact center of the shield. The three rocks or stones are derived from the coat of arms of Pope Pius XII, who established the new Diocese of Rockville Centre in April, 1957. The roundel is tinctured in black to represent the seventeenth century name of Brooklyn, from the diocese from which the See of Rockville Centre was separated. The black tincture represents the marshes, which recalled to the Dutch their homeland in Breuckelen in the Province of Utrecht. The Dutch who first settled Brooklyn called it “Breuck-Landt’” meaning “broken land,’ or “marshland,” inasmuch as a great deal of the land was broken up by patches of water. 

The external ornaments of the shield are composed of the pontifical hat with its six tassels on each side, disposed in three rows, all in green, and the Episcopal cross colored in gold. These are the heraldic insignia of a prelate of the rank of Bishop in accordance with the Instruction of the Holy See of April 17, 1969.