Archibald had two older brothers: Sir John, who succeeded his father; and William, who started the Riddells of Glen-Riddell, in Dumfries-shire.

The Lords of his Majesty's Privy Council having considered a petition presented by Mr George Scot of Pitlochie, desiring that, in regard the Council have granted him the benefit of some persons lately sentenced to the plantations, in order to their being transported thither, and that he is willing to transport Mr Archibald Riddell, prisoner in the Bass, liberty might be granted to him for some time to put his affairs in order, and attend several processes now depending both for and against him before the Session, upon the petitioner's being cautioner for him, that he shall immediately after his liberty, come to his own lodgings in Edinburgh, and confine himself there during his abode here, and, in the mean time, keep no conventicles; and be by him transported to East Jersey in America, and never return to this kingdom thereafter, without special licence from the Council : The said Lords do grant the said desire, and recommend to the Lord High Chancellor, governor of the said Isle of Bass, to give order and warrant to his deputy-governor of that isle, to deliver to the petitioner, or his order, the person of the said Mr Archibald Riddell, in regard the petitioner hath become caution to the effect foresaid, under the penalty of five thousand merks Scots money, in case of failure in any of the premises."

The voyage on the Henry & Francis was disastrous in that about 24 percent of the passengers died including George Scot and Riddell's wife and three of her relations.

[21] In June 1689 he boarded a ship for home, but just off the coast of England, on 2 August, he was captured by a French man-of-war.

His final charge was in Trinity College Kirk in Edinburgh in 1702 which was later demolished and rebuilt due it blocking Waverley Station.

Their daughter, Sarah Bennet Riddell, married Rev John Currie, minister of Oldhamstocks in 1703 who became Moderator in 1709.