James Arthur performed the band's 1996 hit 'Don't Speak' to band members Gwen Stefani and Tony Kanal earlier this week, and won praise from both.
Stefani thanked Arthur for choosing to sing their song, and added after he sang for them that it "was a really hard thing standing there for us".
The 43-year-old singer continued, saying his version was "incredible".
Arthur commented that Stefani was "smoking hot" and that his "heart was going the whole time" while meeting her. He added: "It was a little bit awkward because I was singing their song back to them, but it was a dream come true for me."
Pre-recorded footage on The X Factor also showed Ella Henderson and District3 meeting the No Doubt stars.
Watch James Arthur perform No Doubt's 'Don't Speak' on The X Factor below:
Photo gallery - The X Factor number ones week:
Copyright: Ken McKay/Thames/Rex Features