Generally jewelry is structured as a separate rider on homeowner's insurance -- you just call up your homeowner's insurance company and fax them the appraisals, and they write you a side policy.

If you don't have a homeowner's policy, call a big company like Allstate with the specific question -- "I have seven gems worth $XX -- what policies do you offer and how much do they cost?"

If you are talking very high-end stuff, you might want to go with a company with a reputation for insuring valuable assets -- Chubb does this kind of thing, as does Fireman's Fund. If they're really valuable, the companies might do their own, separate appraisal.

Since your gems are not yet insured, moving them is certainly going to be risky. I would insure them first and then move!

Check with the company about the terms under which you can move them without voiding your policy.