Querrey, ranked No. 19 in the world, succumbed to unseeded and 108th-ranked Jamaican Dustin Brown 6-4, 6-3 in the second round. Brown put the American away with 14 aces and three service breaks, and didn't allow the American a single break-point chance.
Ram took the first set against South African qualifier Raven Klaasen 7-5, but Klaasen rallied to eliminate the American by taking the next two sets 6-1, 7-6 (7-3).
Ram beat Querrey in last year's final.
American Mardy Fish, meanwhile, breezed into the quarterfinals on the Hall of Fame's grass courts with a victory over Somdev Devvarman. The fifth-seeded Fish dispatched the Indian 6-2, 6-0.
Fish will face Canadian Frank Dancevic in the quarterfinals. Dancevic beat Frenchman Nicolas Mahut 7-6 (7-5), 6-3 in the second round.
In other second-round play, Argentine Brian Dabul defeated Japan's Go Soeda 7-5, 6-2. He now meets Brown in the quarterfinals.
The $500,000 event will pay the winner $75,700.
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