[4] Stevenson was knighted on 27 April 1803 by Philip Yorke, Earl of Hardwicke, Lord Lieutenant of Ireland.
In 1843, a marble cenotaph sculpted by Thomas Kirk was erected in the Musicians Corner at Christ Church Cathedral.
Stevenson composed music for the comic opera Love in a Blaze (after Lafont), which was first performed in Crow Street Theatre, Dublin, on 29 May 1799, and The Patriot, or Hermit of Saxellen (1810).
Stevenson's glee They Play'd in Air was performed at the inaugural concert of the Handel and Haydn Society in Boston, Massachusetts, in December 1815.
In 1825, a selection of his cathedral works was printed in two volumes and published by James Power of The Strand, London, with a dedication to George IV.
John Hullah reprinted the concluding chorus The Lord is my Strength from the anthem I am well Pleased in his Singers Library (c.1860), and Joseph Robinson edited three of the twelve together with the unpublished By the Waters of Babylon.