Defending champion Matteo Berrettini will play surprise-finalist Filip Krajinovic in the Queen's final.
Serbia's Krajinovic, who had never won an ATP main draw match on grass before this week, then beat 2018 champion Marin Cilic of Croatia 6-3 6-3.
The rain further disrupted the Birmingham Classic, with both women's semi-finals postponed to Sunday.
Simona Halep will play Beatriz Haddad Maia before Sorana Cirstea takes on Zhang Shuai, with both matches available on the BBC Red Button and BBC Sport website and app.
The Queen's final will take place on Sunday and will be broadcast on BBC One from 13:00 BST.