Yes! ShipStation offers the following options in the Insurance drop-down menu when configuring shipments:
Carrier insurance: Use this option to add the carrier's insurance to your package. Not necessary if you want only the service's default insurance.
Other: Use this option to indicate on your shipment record you have purchased insurance for this package from a third-party insurance provider.
For details on how to use insurance in ShipStation, review the Insurance Options article in the Ship Orders section of the help guide.
How you file an insurance claim depends on what type of insurance you added to the shipment.
If you added Carrier insurance to your shipment, you will need to file the claim directly through the carrier specific insurance portals, linked here for your convenience: