The fictitious Popish Plot (1678 – 1681) caused him some difficulties, but not enough to prevent an appointment as envoy to the Elector of Brandenburg in spring 1680. Southwell's mission involved constructing an alliance against France, and took him to the courts of Orange and Brunswick–Lüneburg, but the notion fell out of favour with Charles II, and Southwell was soon recalled.
Temporarily left in limbo, Southwell busied himself with private and family affairs, improving properties his family had acquired and overseeing the education of his son and other young members of the family. He received an honorary doctorate of civil law from Oxford University in 1677.
In 1685, he was elected to Parliament again, and quietly sided with William of Orange during the crisis of 1688. He had met William during his 1680 mission and may have maintained covert contact. In any case, he readily accepted an appointment as a Customs commissioner in April 1689 and another as principal Secretary of State for Ireland in 1690.
Southwell had been elected a Fellow of the Royal Society in 1662, and while his absences overseas interfered with his attendance at meetings, whenever he found himself in London he participated with enthusiasm. His election as president of the Society in December 1690 can be seen as an acknowledgement of his standing, and his skills as an organiser and diplomat He was re-elected annually until 1695. He died at his estate near Bristol, on 11 September 1702.
Sources: Joel H. Baer, William Dampier (1651–1715); Toby Barnard, Sir Robert Southwell (1635–1702); William Dampier, A New Voyage Round the World; Wikipedia