Consider purchasing an extended warranty. You really have to evaluate this on a case by case basis. Sometimes it's worth it and other times it's not. Consider how much it will cost, how long it will extend the warranty and who will be the owner of the gift. For electronics, it's probably a good idea to invest in the warranty. Just be sure to keep paperwork in a safe place so you can make the claim if necessary. 
 

If shipping a gift, add insurance from the carrier for big ticket items. Insurance from delivery companies is extremely inexpensive, and if you're shipping a valuable item, it's worth it to add it on. 
 

Call your independent insurance agent. Most electronics will probably be covered under your current homeowner's or renter's policy, but valuable jewelry or collectables may need additional coverage. Your agent can advise you toward the best plan to cover these items, whether it be increasing your current policy, adding a rider to it or investing in an umbrella policy. If you're going all out and giving someone a vehicle, that will need its own auto insurance policy.