In a big-hitting encounter it was the Netherlands who ultimately prevailed 22-20 21-15, with the blocking and power spikes of Schuil the difference for much of the contest.
Switzerland did themselves no favours in the second set as needless errors began to creep in.
Next up for Nummerdor and Schuil is an intriguing last-eight clash with Italy's Paolo Nicolai and Daniele Lupo, who stunned the Beach Volleyball world yesterday by knocking out the reigning men's champions Todd Rogers and Phil Dalhausser.
'We played them five or six times and won two or three,' said Nummerdor of Monday's opponents.
'They have played very well and it will be a tough match.'