Mark DelCogliano translated into English the second and third letters that Nestorius wrote to Pope Celestine (published in the original in Loofs, “Nestoriana”) a couple of years ago. As far as I know no other translation in English exists.
He has very kindly sent them to me, for upload onto the web, and has also kindly placed them in the public domain so everyone can use them freely.
The translations are here.