In 1920, Budberg met British author H. G. Wells when he made a celebrated visit to Moscow and they became lovers. She was briefly married, on 13 November 1921, to Baron Nikolai (Rotger Emil Arthur Friedrich) von Budberg-Bönningshausen (born 1896). The union was in the nature of a marriage of convenience, and they soon divorced. (It provided her with a passport, however, and thus an ability to leave Russia to visit both her children in Estonia and Gorky then lived near Sorrento. It is said that the Baron Budberg, a shady character, eventually disappeared in Brazil.) Moura's relationship with Wells was renewed in 1933 in London, where she had emigrated after parting with Gorky. The close relationship continued until Wells's death in 1946. He had asked her to marry him, but Budberg strongly rejected the proposal.