Zimmer, the Royals' first-round pick in the 2012 Draft and their No. 9-ranked prospect according to MLBPipeline.com, made two Spring Training appearances, giving up two earned runs in 2 1/3 innings.
Staumont, who is not on the 40-man roster, gave up one run in three innings over two appearances. He is ranked No. 3 among Royals prospects.
The Royals remain high on both Zimmer and Staumont, and consider them power pitchers who could contribute to the big league team this season.
"It's just a matter of finding them innings," manager Ned Yost said. "We're running out of innings about this time of camp.