Fortunately, music boxes are for the most part very sturdy and well
made, otherwise they would not have lasted the 100-200 years and still
remain in pristine condition.

In moving a musical box you have two concerns: protecting the comb and
protecting the integrity of the motor mechanism.  To do both you need
to make sure that the music box does not start to play uncontrollably
when it may hit a bump in the road.

First thing to do is you need to "let down the spring".  If the music
box has a Geneva stop, remove it at this stage and secure it someplace
where it will not be lost and will remain with the correct box.  Allow
the music box to play to the end of the spring, then release the pawl
and wind the spring backward to remove the remaining pressure in the
spring.

I heard of a case where someone wanting to protect a music box took
this one step further and removed the spring barrel to ensure it had no
tension, then shipped it loosely placed inside the box, causing broken
teeth when it bumped around during the journey.

If the musical box has interchangeable cylinders, remove the cylinder
during transit.  Protect them and ship them outside of the musical box.

Wedge a half-cork between the cylinder and the spring barrel if it's
remaining in place, and do anything simple to ensure that the butterfly
can't spin if released (tape a piece of paper there to stop it).

Finally, place a piece of strip magnet along the comb.  This joins all
the teeth together and like the familiar story of breaking one pencil
easily but being unable to break a group of pencils, it helps to
protect the comb from damage.

I once thought it would be a good idea to remove the comb and ship them
separately, but there is often small irregularities when you remove and
replace the comb so it's better to leave it in place if possible.

Eli Shahar