Holders Leeds Rhinos were defeated in round three by St Helens, whose tie with Huddersfield Giants will be shown live on Sky Sports on Friday 7 May (8.15).
Prior to that, Catalans Dragons face Warrington Wolves also on Sky Sports (6.00).
Coverage switches to BBC on Saturday May 8, with BBC1 showing Hull FC versus Wigan Warriors (2.30pm), and Castleford and Salford going head-to-head live on BBC2 (5pm).
RFL chief commercial officer Mark Foster said: “We’re delighted to be able to confirm that all four Quarter Final games will be broadcast live, and our thanks go to our broadcast and commercial partners for their continued support of Rugby League.
“The broadcasters have been extremely helpful in ensuring that all these games are televised and on successive days.
“Like last year, all Quarter Final matches are being played at a neutral venue, based on availability and suitability.
“In this case, Emerald Headingley Stadium offers a perfect venue for what promises to be an exciting round of matches.
“The two Round Three games shown by BBC last weekend drew the highest viewing figures for this particular round for four years, so we’ll be looking to maintain this momentum throughout this year’s competition.”
Betfred Challenge Cup Quarter Final Draw
Castleford Tigers v Salford Red Devils Saturday 8 May, 5pm
Catalans Dragons v Warrington Wolves, Friday 7 May, 6pm
Hull FC v Wigan Warriors, Saturday 8 May, 2.30pm
St Helens v Huddersfield Giants, Friday 7 May, 8.15pm