Cibulkova is due to marry fiance Miso Navara in her hometown of Bratislava on Saturday.
But the confetti and wedding cake might be put on hold because the Slovakian 19th seed has advanced to the quarter-finals with a 6-3, 5-7, 9-7 victory against Radwanska.
Cibulkova's walk down the aisle will have to wait if she defeats Russian world number 50 Elena Vesnina in Tuesday's quarter-finals.
Federer reached the quarter-finals for the 14th time as he edged closer to a potential dream title match with Andy Murray.
Second seeded Murray, the 2013 champion, eased to a 7-5, 6-1, 6-4 win over fiery Australian Nick Kyrgios and will next face French 12th seed Jo-Wilfried Tsonga.
Federer went equal with Jimmy Connors' mark of 14 quarter-finals at Wimbledon and tied Martina Navratilova's all-time grand slam record of 306 match wins by seeing off Steve Johnson of the United States 6-2, 6-3, 7-5.
Seven-time champion Federer, the third seed, next takes on Croatia's Marin Cilic for a place in the semi-finals.
Cilic, the ninth seeded Croat, progressed to his third successive Wimbledon quarter-final when Japanese fifth seed Kei Nishikori pulled out of their last-16 clash with a rib injury in the second set.
Federer has a 5-1 record over Cilic but the big-server stunned the 17-time major champion in the US Open semi-finals in 2014 on his way to his maiden grand slam title.
"He blew me off the court and I hope to get him back," said 34-year-old Federer.
Sam Querrey followed up his shock defeat of defending champion Novak Djokovic by beating French veteran Nicolas Mahut 6-4, 7-6 (7/5), 6-4 to reach his first major quarter-final.
Querrey, the 28th seed, is the first American in the last-eight at Wimbledon since Mardy Fish in 2011.
Querrey will next face Canadian sixth seed Milos Raonic, who came back from two sets down for the first time in his career to beat Belgium's David Goffin.
Raonic, a Wimbledon semi-finalist in 2014, won 4-6, 3-6, 6-4, 6-4, 6-4.