Singapore - Shipment insurance
This can be most easily done with the removal company. Understand the cover that is offered and read the small print. Check if the insurance covers the replacement value.
Compile your own inventory with a detailed description of expensive items. Assign a realistic replacement value to each item. Some people take photographs especially of antiques and other items of high value.
Even better ask for precious items to be estimated and have a printed evaluation to present to the shipping company.