How much will I be charged for an estimate?

"

Out-of-Warranty Service

If you own an iPhone that is ineligible for warranty service but is eligible for Out-of-Warranty (OOW) Service, Apple will service your iPhone for the Out-of-Warranty Service fee listed below.

A $6.95 shipping fee will be added if service is arranged through Apple and requires shipping. All fees are in U.S. dollars and are subject to local tax. "

Apple wil not give you a quote per se since they don't have any variable pricing. They charge a flat replacement fee for any non-warranty failure or damage. So there is no quote to give. Just give your insurance company a printout of Apple's out-of-warranty repair page, which can find in the Warranty and Service Pricing section here:

http://www.apple.com/support/iphone/service/faq/

or as Tim suggested visit an Apple Store and get them to give you an official pricing statement of their replacement charge.

Regards.

You pay nothing for the quote. It is posted in 2 messages already. THAT is the quote.

You must pay for the iPhone 5 $229 and for the iPhone 4S $199

What quote... just make an appointment at the genius bar. Ask them for a written statement for the replacement cost for your insurance company...