IBM System/360
From Computer History Wiki
The System/360 is a groundbreaking mainframe computer introduced by IBM on April 7, 1964. It ran a variety of software, such as MVS.
The System/360 was supplanted by the System/370.
Emulation
I don't think there is any direct S/360 emulators out there... However I'm pretty sure that Hercules will run System 360 software as the 370 is upwards compatible with the 360.