DISCLAIMER: IF YOU SET THE GH4 TO 0-255 or 16-235 THERE IS NO PROBLEM!
This Premiere Pro tutorial shows you how to recover clipped highlights when shot in the default 16-255 mode on the GH4. This only addresses highlights that were not clipped on the sensor itself but by the YUV to RGB conversion. This methods also works for any other camera that uses superwhites, and there's a lot of them out there...
Most footage from the GH4 contains so called superwhite data that clamps to detail-less white when not treated correctly.
This is because by ITU.709 regulations a YUV decoder expects white to be set at 235 (which will map to 255 RGB), but the GH4's white is standard set to 255 to have more room to play in grading. If you don't bring those values down everything over 235 will be bluntly cut off when playing directly or uploading it to Vimeo resulting in harshly clipped highlights.
Note: not all color correction tools can handle the YUV superwhites/superblacks, I only know for certain that the Fast Color Corrector can.