The Ayrshire club face the Scottish champions knowing that, after a League Cup exit to Airdrie, a second defeat in a week would take the shine off their manager's reward for making them a Premier League force. Not that Williamson intends to dwell on his achievements in guiding Killie to a Scottish Cup win, fourth place in the league and two successive European campaigns - he is currently overseeing plans for a pounds 6m youth development complex at Rugby Park.
"I want to make sure this club is up there challenging," he said. "But nobody has got the right to be there and we know we have got to continue to work hard if we are going to build on what we have done.
"We showed a level of consistency last year, and got the bit of luck that you need, and I am confident we can do the same again this time."
A win over the champions would be another worthy addition to the Williamson CV, but the pre-match preparations of the Celtic coach, Jozef Venglos, have not been helped by the news that the midfielder Morten Wieghorst could be out for the rest of the season. At least the strikers Henrik Larsson and Darren Jackson appear to have returned home unscathed from international duty.
The Hearts defender Paul Ritchie has been given the all clear to play against Dundee today after his red card against Ross County in midweek was rescinded by the Scottish Football Association. Ritchie was sent off in error following an off-the ball incident involving Derek Adams. Heart's Steve Fulton later admitted he was the other player concerned.