That is in stark contrast to the women's event where second seed Kristina Mladenovic suffered a 6-3 6-1 quarter-final defeat to Ukraine's Lesia Tsurenko.
Top seed Dominika Cibulkova fell in the first round.
World number seven Cilic recorded his 50th grasscourt match win, beating Vasek Pospisil 6-3 7-5.
"I feel better and better, obviously after each day I'm getting used to the grass," Cilic, who recovered a 5-2 second-set deficit, said. "I served well in critical situations."
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The 38-year-old Karlovic reached his first semi-final of the year after the third seed beat qualifier Daniil Medvedev 6-4 6-4 in less than an hour on court.
"I was playing unbelievable, with some really good volleys. Overall I am happy with the performance," he said.
Zverev, 20, was also detained for less than an hour as he beat 35-year-old Frenchman Julien Benneteau 6-0 6-4 while Mueller beat Britain's Aljaz Bedene 6-3 3-6 6-4.
Mladenovic, a 2016 runner-up, struggled throughout against Tsurenko, making 24 unforced errors to her opponent's nine.
Tsurenko will meet Estonia's Anett Kontaveit while the other semi-final will be between Croatia's Ana Konjuh and Russian Natalia Vikhlyantseva.
(Reporting by Martyn Herman; editing by Mark Heinrich/Alan Baldwin)
