In our hospital, the radiology techs are responsible for bringing the renal biopsies up to the department (in saline) as soon as the procedure is obtained. They show the specimen to the attending pathologist, who signs off on the radiology record as sufficient. Then the histotechs divide the specimen for the EM, IF and NBF specimens.
Our muscle/nerve biopsies are all done in-house up in OR and are sent directly to the lab in a dumbwaiter "fresh"  on saline-soaked gauze where the histotechs then divide up the specimen according to protocol. The nurses are responsible for delivery to the histology department.