During part of his time abroad, he was employed as a royalist agent in Germany and Denmark, in company with Lord Wentworth, until the partnership was dissolved by a violent quarrel, leading apparently to a duel.
During the negotiations at Breda, he found time to write a heartfelt letter of condolence to his old friend Lord Clarendon on the death of his wife Frances Hyde.
When the King, who was determined that Clarendon must fall, expressed his displeasure at his known wishes in the matter being defied, Henry with his usual frankness replied that if he could not speak his mind in Parliament, he had best not go there at all.
[3] He was a capable administrator, who built up an efficient intelligence service: even the most minor complaints against the Crown, such as the "curse on the King for his bad example to other husbands", uttered by the wife of the town gaoler in Newcastle upon Tyne, came to his attention.
During the Popish Plot, while the nerve of his colleague, Joseph Williamson, cracked under the strain, Coventry generally maintained his composure, but he was concerned at the public hysteria: "the nation and the city are in as great a consternation as can be imagined".
During the Exclusion Crisis, he was one of the first to warn that any attempt to bar the Duke of York from the succession might lead to civil war: "if that Prince go into another place, it must cost you a standing army to bring him back".
He had "an unclouded reputation" for honesty: it is to his credit that after holding public office for nearly 20 years he had not accumulated any large fortune; though no doubt in easy circumstances, he wrote of himself as feeling straitened by the loss of his official salary on 31 December 1680.