Swardeston will face either Acle or Dereham in an away trip in the second round of the Bob Carter Cup on 29 May.
Meanwhile, the big guns from the Gibbs Denley East Anglian Premier Cricket League have avoided each other in the draw.
Vauxhall Mallards, the holders, will entertain Diss or Horsford if they beat Fakenham in their postponed first round match, a repeat of last season’s final. Norwich will be at home to Old Buckenham.
Other pairings: Bradenham or Cromer v Brooke, Great Witchingham v Saham Toney, North Runcton v Sprowston, Saxlingham or Sheringham v Beccles and Topcroft v Sprowston.