In 2004, Oberman became engaged to music producer Rob Cowan. The couple were honeymooning in Thailand when the 2004 Indian Ocean tsunami struck. In an interview with The People, Oberman described the experience as "one of those crystallized moments in my life. Its made me focus on the people I love. It also showed me the incredible generosity people are capable of. When you have seen something like that, you also stop taking the trivia so seriously".
In 2005, Oberman was cast in Mike Leigh's play Two Thousand Years at the National Theatre but had to drop out when she became ill. In August 2006, Oberman gave birth to a girl, Anoushka India, at a Central London hospital with her husband Rob Cowan by her side.