insure against something
to guard or protect against something. You must insure against theft and fire. I will insure against all risks.
insure someone or something (against something) (for something)
to provide insurance for someone or something against certain perils up to a certain amount of money. I insured my wife against accidental death for $100,000. We insured the car for its current value against all losses.
insure someone or something with something
to provide insurance for someone or something from a specific company. I insured Amy with a fine old insurance company. We insured the car with Acme Insurance in Adamsville.