In short, Brent nailed it, it will really come down to how the item was packaged.
The coverage will cover lost and damaged items, however, as Brent stated, they need to be packed very well. UPS has very strict requirements that a package must meet in order for the contents to be covered for damage. The items must have sufficient padding around and between items and at least 2”-4” of padding between the items and the walls of the box. This padding should be small or large cell bubble, air pillows, expanded polystyrene peanuts or foam sheeting. Newspaper is not approved and will void the coverage. The box must be a new durable corrugated shipping box, 200# - 250# bursting strength depending on the overall weight of the package. Smaller lightweight items can utilize a 32# edge crush box. Most Home Depot and U-Haul boxes do not meet these requirements and the claim will be denied. Reusing an old beat up box will also void a claim.
When an inspection is made, all of the contents and packaging materials must be present. The inspector will examine the materials to determine if they were sufficient and met the requirements. They will also determine if the damage was caused externally from something penetrating or crushing the box, or if the damage was initiated internally from items inside moving around causing damage due to lack of materials.
As far as loss goes, if the package goes missing in transit and there is no delivery scan, they will do a lost package investigation. If the package cannot be found after 8 business days then you will be reimbursed for the declared value as long as you can prove the value. If however there is a delivery scan, then it is hit or miss. If they can prove the package was delivered and to the correct address, then the problem is considered a theft and must be taken up with local law enforcement. If however you can reasonably prove that the package was never delivered or delivered to the wrong address and not retrievable then you have a good chance for reimbursement.
I have dealt with many damage and loss claims and it really can be a crap shoot. Lower valued items, typically valued under $100, seem to have a bit more leniency. Higher value items require more of a battle. It will all come down to how well the item was packed and what materials were used to pack it.
In rocket1’s case, the agent was incorrect. You can declare whatever value you want to cover an item for, however if something happens to the item, you will need proof of value. A receipt, an authorized appraisal, or comparable item, etc.. If a claim is honored and the item is repairable, you will need to prove the cost of the repair. The payout will be the lesser of replacement vs repair. Keep in mind that if the payout covers the replacement, then the item becomes property of UPS and must be surrendered upon payout.
UPS Declared Value Q and A
Preventing Claims
Packaging Advisor