Yes, if the postage cost is included in the declared value and the claim is approved Shipsurance will refund the cost of the postage as part of the claim reimbursement.
NOTE: It is not possible to file a claim to only recover the cost of the postage or shipping and handling. It is only recoverable if it is part of the declared value and there was a total loss or damage to the insured shipment while in transit.
How to: File a claim with Shipsurance
How to: Check the status of my Shipsurance claim
What to do if a package is returned due to not enough postage?
Can I get a refund on postage for returned items?
What happens to the insurance charge for a cancelled label?