Dancevic, seeded seventh, upset fourth-seeded Russian Igor Kunitsyn 7-5, 6-3 and Amritraj, of India, topped countryman Rohan Bopanna 6-4, 6-3.
The two winners will meet in the semis.
Defending champion Fabrice Santoro, who had an opening-round bye in the grass-court event, won a second-round match to reach the quarterfinals. The 35-year-old Santoro, seeded second, beat Aisam Ul-Haq Quereshi of Pakistan 7-6 (7-4), 6-2.
American Vincent Spadea eliminated third-seeded Frenchman Nicolas Mahut 6-2, 6-3 to gain a quarterfinal berth.
Others advancing to the quarters were Austrian Alexander Peya, who ousted American Donald Young 7-6 (7-4), 6-3, and Spaniard Ivan Navarro, an 7-6 (7-3), 3-6, 6-4 winner over South African Kevin Anderson.
Celebrity Families of 2014 [PHOTOS]