Smith performed at the Canadian festival for four seasons between 1976 and 1980, performing Shakespearean roles such as Cleopatra in Antony and Cleopatra, Rosalind in As You Like It, Beatrice in Much Ado About Nothing, Mistress Overdone in Measure for Measure, Queen Elizabeth in Richard III, Titania/Hippolyta in A Midsummer Night's Dream and Lady Macbeth in Macbeth.
Her non-Shakespeare roles during this period included Masha in Three Sisters, The Actress in The Guardsman, Judith Bliss in Hay Fever, Amanda Prynne in Private Lives, Irina Arkadina in The Seagull and Mrs. Millamant in The Way of the World, for which she won her second Variety Club Best Actress Award. She also played the title role of the world première of Edna O'Brien's Virginia, with that production going on to the Theatre Royal Haymarket, winning Smith her first Olivier nomination and her second Evening Standard Drama Award for Best Actress.
Among Smith's dozens of awards are a Tony and an Olivier, two Oscars, seven BAFTAs, two Emmys, two Golden Globes, a SAG award and five Evening Standard Theatre Awards. She was awarded the Hamburg Shakespeare Prize in 1991, is a fellow of the British Film Institute, was awarded a Silver BAFTA in 1993, is an Hon. DLitt of Cambridge University, and St. Andrews, and is a patron of the Jane Austen Society.
In a statement, Stratford's Artistic Director Des McAnuff commented, "One of our Festival's founding principles was that we should be a home for artists of international stature as well as for our own Canadian stars [. . .] Her performances on our stages made an immense contribution to our artistic legacy and are still treasured in the memories of all who experienced them."