She said: "They would have been best friends, she would have been delighted because she got her daughter. She always wanted to have a little girl, and to share clothes and things, and she would have had her daughter-in-law."
Sarah - whose daughters Princess Beatrice, 22, and Princess Eugenie, 21, attended the wedding with their father Prince Andrew - also praised the Duchess of Cambridge for her "serene" attitude.
In an interview on CNN's Piers Morgan Tonight, she added: "I take my hat off to Catherine [Kate], she's so serene. She floats like a swan. I'm a great fan. I think she's able to cope with the pressure. She has a very good family, I don't know any of them, but they all look so together and solid.
"And she knows, because they've been dating nine years... I think she's doing brilliantly. And I think that she so loves him."
Sarah admitted while she was "so upset" not to have been invited to the nuptials, she was "taken in" by William and Kate's love story.
She said: "I was so upset, but so happy for William and Catherine. I was taken in by the love story. And I remember the love story Andrew and I have... had or have."
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