The present disclosure relates to an improved process of organ perfusion with vitrifiable concentrations of cryoprotective agents. In one implementation, the method may include perfusing an organ with a first solution containing a vitrifiable concentration of cryoprotectant at a temperature at or above −;10° C. and perfusing the organ with a second solution containing a higher concentration of cryoprotectant than the first solution. The first solution may be adapted to vitrify at a cooling rate of less than 20° C./min, and the second solution may be adapted to vitrify at a cooling rate of less than 5° C./min. The perfusing with the second solution may begin at or above −;10° C. and cause the organ to decline in temperature to below −;10° C.