McKendrick was named as one of the Poetry Society's 'New Generation' poets in the 1990s, with the Society selecting his 1997 collection Marble Fly as a Poetry Society Book Choice. Marble Fly also won the 'Best Poetry Collection of the Year' award at the Forward Poetry Prize ceremony.
Other awards that he has won include:
2010 Oxford-Weidenfeld Translation Prize for Valerio Magrelli’s The Embrace
2003 Society of Authors Travel Award
1994 Southern Arts Literature Award
1991 Arts Council Writers' Award
1984 Eric Gregory Award
In addition his collections have been shortlisted for various awards, including the 2003 T. S. Eliot Prize and the 2003 Whitbread Poetry Award.