Griemink, 27, is joining Swindon Town on a month`s loan as cover for Frank Talia.
"Jimmy was desperate for a goalkeeper," said Posh boss Barry Fry. "I had no hesitation in lending him Bart."
Broughton, 21, has joined Conference side Nuneaton Borough, also for a month.
The former Norwich player has been allowed to leave to gain some match practice nad to get his confidence out.
Graeme Bailey