I actually own two real mainframes. They're both coprocessor boards for Micro Channel systems, but they're real IBM mainframe processors and run real IBM code. I've used one, a P/390, for the past few years. This one runs reasonably recent mainframe operating systems, and is reasonably fast.
The other is a P/370. This was the previous generation, and the first board of its kind that ran real IBM software with no modifications needed. (IBM made two prior boards, the XT/370 and AT/370, but those required major modifications to the OS running on them.) I was given the P/370 many years ago by a guy who didn't need it any more once Hercules got good enough to fulfill his requirements. I retired it when I got the P/390, as well as the computer it resided in.
Both boards need a host system to provide I/O and such. The usual system was a PS/2 running OS/2, but they also could be installed in an RS/6000 running AIX. The P/370 needs a system with AIX 3.2.5, dating from 1994; the P/390 will run up through AIX 4.3.3, from 2000. Because of this, only one of my RS/6000s will work with the P/370.
I got the old system reloaded a couple of nights ago, and finally got the P/370 running a little while ago. I'm taking a full system backup now. Next time I find myself needing to reload the box, I won't have to work anywhere near as hard.
I've got another RS/6000 coming soon, and have a P/390 board to stuff in it as well. The datacenter will then have 3 real (non-emulated) mainframes, as well as a lot of other stuff. Whee.