The Wolves won the competition in 2009, 2010 and 2012, but missed out on a trip to Wembley last season when they were beaten 16-12 by Hull in the semi-finals.
They take on Bradford in the quarter-finals at Odsal on Sunday, looking to reach the last four once again.
Higham said: “We have had a good few years in the Challenge Cup but we fell at the semi-final phase last year which was really disappointing.
“It was really difficult watching the final as I kept thinking we should be arriving at Wembley around now and we would be coming in from the warm up about this time. Not being there has definitely spurred us on this year, we want to be there at Wembley.
“You can’t get tired of winning the Challenge Cup: it’s not possible. It’s something you want to experience as many times as you can and each time is special as you have a different set of players with you which makes it great.”
Warrington faced the Bulls in Super League in early May which ended with the Bulls emerging victorious so Higham is expecting a tough game on Sunday.
He said: “When we played them about a month ago we underestimated them and they beat us 34-28. I think we are playing better than that now but we both had good results at the weekend so both teams will be going in to the game with confidence.
“We will prepare as normal as if it is just another game but deep down you know that it isn’t just a normal game and potentially you could be one game away from Wembley. You try and blank out those sorts of thoughts but it is really difficult because it is such a special competition.”