Emms said: "I know that could be possible and it's is hard to not think 'well, if we beat them then it's going to mean one more win and you know what' but the Danes played really well to beat the South Koreans."
Emms and Robertson beat Chinese pair Chen Qiqiu and Zhao Tinting 15-8, 17-15 and are guaranteed a shot at the bronze to emulate Simon Archer and Joanne Goode's achievement at the Sydney Olympics.
The pair had contrasting fortunes with other partners. Emms recorded a first round victory in the women's doubles alongside Donna Kellogg, but Robertson and Anthony Clark lost to Indonesia's Eng Hian and Flandy Limpele 15-7, 15-12.
In the men's singles, Richard Vaughan won his first round match 15-5,15-3 against Portugal's Mareo Vasconalos.