Before actually starting the recording, I put some transparent plastic around the lens, between the cameras, to make the lightning more even. Here is the outcome, in an animated GIF:
See also the full movie here, for more details:
This looks very impressive, of course. But does it work? If you use a Panasonic lens, with built in Optical Image Stabilization, you must make sure to set the "Lens I.S. Priority" item to "Off", you'll find it in the C-section of the rather confusion menu.
If your lens has an OIS switch, you need to set that one to off as well. If not, the camera will try to use the lens image stabilization, which is not as effective.
Using the Lumix X 12-35mm f/2.8 lens, I recorded this handheld example video. Even when walking around with the camera, the video is remarkably stable. For even better effect, I could have added some Warp Stabilizer in the Adobe Premiere Pro, but even without additional software stabilization, the video is very smooth:
If I had used the same lens on the Lumix GH4, the results would have been far less stable. See a direct comparison between the two cameras here.