On 23 March 1461 he received papal provision to the bishopric of Ross vacant by, presumably, the death of Thomas de Tulloch.
[1] He was consecrated sometime between 19 October 1463, when his name occurred in a Dunfermline Abbey document as bishop "elect and confirmed", and 16 August 1464, when he witnessed a royal charter as consecrated bishop.
[3] Bishop Cockburn was sent as part of an embassy to the Kingdom of England in 1473.
[5] The episcopal see of Ross was vacant by 20 August, suggesting that Bishop Cockburn had died at some stage between 22 July or 20 August and although resignation or demotion is a possibility, there is no evidence pointing to such a highly unusual and notable occurrence.
[6] Henry Cockburn, as a cleric and prelate, was forbidden from marriage, but he is known to have had at least one son, John Cockburn; John was legitimised on 20 September 1507.