In WooCommerce and its shipping options, there is not a built-in way to offer insurance for goods you are shipping.
Include in product price
One option is to include the insurance cost in the price of your products. This, however, has the downside that it gives customers the wrong impression on actual cost of a product.
- If the insurance is optional, you can use this code example from Stack Exchange. It allows the customer to choose whether to use shipping insurance or not.
- If the insurance is not optional, our Payment Gateway Based Fees extension may work better. This allows you to add a cost to the payment method to charge an extra fee.