Houston - Shipment insurance

There are two shipments considered here, shipping in or out of the country and moving within the US.

To ship your belongings either in or out of the States, use the estimate provided by the ship for a starting point and make sure you have accounted for all your belongings taking into account the various situations such as damage in transit, breakage or loss. 
It is worth contacting your present insurers that you use for your home and contents as this may just involve a policy cover change rather than starting from scratch.
It is also worth asking the company that you choose for the shipping as they may have insurance specialist suggestions.
Do ensure that you understand each of the options open to you - understand the cover and how the cost is broken down.
Read all the literature carefully and do ask questions, you are in a weak position to negotiate at a later point if you haven't read the small print.
 
By law in the States, when moving within the country, the removal company has to include an amount per pound which is free to you. However, even with national movers, this is a minimal cover and will not cover you above the quoted value per pound in weight. You should therefore have additional cover arranged which realistically covers the actual value of your belongings for loss or breakage.
As in the case above, contact your present insurers that you use for your home and contents as this may just involve a policy cover change rather than starting from scratch.
It is also worth asking the removal company that you choose as they may have insurance specialist suggestions.
Do ensure that you understand each of the options open to you - understand the cover and how the cost is broken down.
Read all the literature carefully and do ask questions, you are in a weak position to negotiate at a later point if you haven't read the small print.