Boro's reward for last night's 4-0 win at Tring Athletic is a trip to Top Field to face Hitchin.
The Canaries came back from 3-0 down against Hoddesdon Town on Monday to draw 3-3, before going on to win 3-2 on penalties.
The two sides last met in July in a pre-season friendly when a Stevenage team comprising squad players, trialists and youngsters ran out 5-0 winners, with Dani Lopez notching a hat-trick.
Herts Senior Challenge Cup Quarter Final Draw
Hemel Hempstead Town v Hertford Town or St Albans City
Boreham Wood v Potters Bar Town or Watford
Hitchin Town v Stevenage
Bishop's Stortford v Barnet
Ties to be played w/c 20th January with an exact date to be confirmed.