One way that works is to buy yourself an external usb drive. They are cheap now, and you can get a housing for a laptop drive that doesn't need mains power.
a 30gb drive should be more than adequate!
The copy the existing pst file onto the usb connected drive, and do a clean set up of outlook. That way you have a blank pst file on you r main hard drive on both computers.
Then, on one computer, plug in the usb drive and tell outllok to open an extra pst file. Modify the order of searching contacts, etc to use the usb pst file first ( or you could even delete the small pst file)
Close outlook, go to the other machine and repeat the sequence.
You should now have a "portable" outlook pst file.