The fourth-seeded Verkerk, of the Netherlands, beat Swiss qualifier Michel Kratochvil 6-3, 7-6 (7-0).
Verkerk will play Rochus, of Belgium, who eliminated another qualifier, German Alexander Waske, 3-6, 6-3, 6-4.
Davydenko, a Russian who lives in Germany, moved into the semis by knocking out the tournament's top seed, Rainer Schuettler of Germany, 6-1, 7-6 (7-4).
"I controlled the ball well and he couldn't attack me," Davydenko said. "It was a good match for me."
Davydenko will play Peruvian Horna, who advanced with a 7-6 (8-6), 7-6 (7-2) win over Radek Stepanek of the Czech Republic.
2014: The Year in Music [PHOTOS]