I recently bought a very expensive engagement ring from a local
jeweler, and they offered to keep the three GIA certificates on file
for me (so I don't misplace them).  Is this a common practice?  Should
I trust my jeweler or store them myself?

What is important is that your insurance company has copies...not
really where the originals are...personally I have scanned mine into
my computer and put on disc in the house/gave copies to insurance/put
originals in safe deposit box (In Canada a safe deposit box is an
investment cost so you can write it off your taxes anyway)...all
covered...why keep it with a jeweller that may go out of business?

Certified diamond engagement ring certificate should be listed with
your insurance company, as well as having the original in a safe
secure location. You may want to make an extra copy to keep elsewhere
just in case, such as your parents home,etc. But by all means
insurance on your ring is a must, as well as a every two year check by
your jeweller for loose prong settings.

Best Wishes
LBJewelry

http://www.lebaubles.com/certified_diamond_ring.htm