Below are two citations. I see some bad genealogy claiming he is related to Archbishop of Canterbury Cranmer. His son William was born quite a bit earlier and his marriage to someone else well-documented. The last citation says the relationship is neither proven nor disproven but I would say entirely unproven and not to be mentioned absent actual documentation (of which there seems to presently be none).
Department of Notes and Queries" Somerset County Historical Quarterly vol. Vp. 236: CRANMER--" ...William Cranmer came over from England and was at Southold, L. I. in 1640, and at Elizabethtown in 1665; wife Elizabeth Carwithy, whom he married at Southold. He owned at Elizabethtown various tracts amounting to 209 acres, and a town lot of six acres on which he lived. He d. in 1689. His sons were Thomas, William, Josiah and John. William settled at Barnegat, and John at Whippany, Morris Co. John a son of William, whose wife was Sarah Osborne, had sons Josiah, Nathan and William...... "
Excerpted from Descendants Of William Cranmer Of Elizabethtown, New Jersey by Jean Shropshire Harris And Murray Thomas Harris. Published by the Gloucester County Historical Society, Woodbury, NJ.
William Cranmer, the progenitor of the Cranmer/Cramer families of the Jersey shore, first appears as one of the early settlers of Southold, Long Island, New York. Before 1665 he married Elizabeth Carwithy, daughter of David and Grace Carwithy of Southold. David Carwithy's will, written 30 August 1665 mentions his daughter Elizabeth Cranmer. William and his family must have already moved to Elizabethtowne, New Jersey, because William Cranmer is recorded as having taken an oath of allegiance and fidelity to the King of England at Elizabethtowne on 19 February 1665 and was probably one of the original settlers. He gave his occupation as carpenter, and paid quitrents on 209 acres of land at Ellzabethtowne in 1670, the same year he was appointed town constable there. In 1677 William sold several parcels of upland, together with his dwelling house and house lot, to John Toe and traveled to Lewes, Delaware, with Luke Watson, another of Elizabethtowne's founders. He died before 4 December 1689, when the administration of his estate was granted to his son Thomas Cranmer of Elizabethtowne. There are accounts of William Cranmer's relation to the famous Archbishop of Canterbury who was burned at the stake in England. but to date no evidence has come to light which would prove or disprove this connection.
