Best methods I have found
[1]
Don't zoom while shooting. Zoom then shoot.
[2] Disable Movie SR (even if hand held!!)
[3] Disable AF during video.
[4] Try not to pan quickly, always better to let the scene provide the movement - not the camera
[5] In the picture style, remove sharpness completely (full minus - )
[6] Removed contrast completely (full minus - )
[7] Reduce saturation
Buy a monopod
Here's a couple of my [very amateur] MX-1 clips (watch at 1080p):
Hand held, very slow pan: 1cm Macro test. Hand held - slow movement