Williams lost the first 6-3 on Centre Court.
With Angelique Kerber also having made the last four, it is the first time two German women will play in the Wimbledon semi-finals since 1931.
Her star power grew during a match against Serena Williams in the quarterfinals when she won the opening set and challenged in the third.
Cibulkova did her best to try and hang on but the Slovakian was left chasing shadows as Ostapenko blasted a backhand victor on her first match point to reach the last four without dropping a set in this year's tournament.
Goerges, seeded 13th, faces seven-time Wimbledon champion Serena Williams on Thursday for a place in Saturday's final.
On Wednesday, Federer will play No. 8 Kevin Anderson, a South African who was the 2017 U.S. Open runner-up and advanced with a 7-6 (4), 7-6 (2), 5-7, 7-6 (4) victory over Gael Monfils. When she served for it a second time, she needed to navigate a 16-point game that included five deuces and all of those match points, until forcing a forehand error on the last.
Even when Serena was on the brink of losing the set, she managed to hit a 122 miles per hour serve, her fastest of the tournament. Bertens is seeded 20th.
Through her four Wimbledon matches last week, Williams carefully had calibrated the speed of her serves, taking care not to aggravate the injured pectoral muscle that had forced her withdrawal midway through the French Open last month.
Told she is guaranteed of rising to 51st next week - and higher if she reaches the final or wins the championship - Williams joked: "Got to keep trekking on, though".
Bertens, a French Open semi-finalist in 2016, is into the Wimbledon quarter-finals for the first time.
"You never know what to expect from her [Ostapenko]", Cibulkova said. "Everybody has the same chances to win that match, and I'm looking forward to it".
Williams took the set in convincing fashion, 6-3, and yelled her trademark, "Come on!" as she clinched the final point.
Serena is the first woman to reach a Grand Slam semifinal without facing a top 40 ranked opponent since 2013.
"I don't want her to have pressure from what I did, you guys talking about, 'are you going to be able to do as good as your mom?' I don't want her to have that".
"The more I can just treat it like another tennis match, the better for me". She won 44 of the past 54 points she served.