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It will depend on the insurer of course but you will probably need an appraisal in addition to the purchase receipt.
The good news is that if you are insuring several pieces you can probably get them appraised all at once -- ask a local jeweler what his fee would be for this kind of consultation, or you can call up one of the big department stores -- I know Macy's jewelry department used to offer appraisals, for instance.
For new jewelry, a sales receipt, photo and appraisal are often required if you chose to do an individual schedule. Usually, this schedule is a rider to your home/renters policy and frequently insurers will require that you hold one of these policies with them. For older jewelry, an appraisal is often required.
Be sure to check with your insurer, as the company may have recommended appraisers as well as details over blanket coverage (all pieces under a specific value) or a schedule (pieces itemized and individually appraised).