[2] He was awarded a Bachelor of Arts at Oxford on 13 October 1638 and in 1639 he was elected Fellow of All Souls' College, where he lived during the English Civil War.
As a royalist he was deprived of his fellowship by the Parliamentary Commissioners in 1648, but an application on his behalf to the wife of Thomas Kelsey, deputy-governor of the city of Oxford, accompanied by "certain gifts", secured his speedy reinstatement.
Bliss, p. xxv) as joining in 1655 a number of Royalists "who esteem'd themselves either virtuosi or wits" in encouraging an Oxford apothecary to sell "coffey publickly in his house against All Soules Coll".
At the Restoration, Baldwin was nominated a royal commissioner to inquire into the state of the university and was admitted principal of Hart Hall, Oxford (now Hertford College) on 21 June 1660.
This very rare tract treats of the charge of manslaughter preferred in an English court against Don Pantaleone, brother of the Portuguese ambassador.
In 1663 Baldwin edited and published The Jurisdiction of the Admiralty of England asserted against Sir Edward Coke's "Articuli Auctoritatis" in xxii.