Swans boss Carlos Carvalhal will face his old club again at the Liberty Stadium the week after next as they bid for a last-eight place for the first time since 1964.
Wayne Routledge and Jordan Ayew went close for the visitors in the final 20 minutes but Wednesday had the last chance, although Lucas Joao was flagged offside as he attempted to turn in Adam Reach's cross.
Carvalhal was given rousing ovation by the home crowd at the end of today's stalemate.
“I almost cried after the game when two fans came to talk to me," Carvalhal revealed.
“It's a very emotional moment for me. I must say thank you to Sheffield Wednesday – to the fans, the staff, the manager and the players – for the way they received me.
“They all treated me very well and this is a part of football I love.
“The fans were unbelievable. I know if a player or manager works hard and gives 100 per cent to the club, they will recognise this.
“I felt that today and I am very proud. This is a moment which I will always remember. It makes me the happiest manager in the world."