Not sure where you'll stand re the imprecision around the watch model, but you would hope that having the box and papers would be adequate for their purposes. In my experience home insurance is more sensible and sympathetic than car insurance. When I was burgled they instantly offered me the replacement cost of the items stolen; and if yours is offering replacement cost then the market value of the watch - it was a specified high-value item, rather than an agreed-value one - isn't really relevant.
The one catch - to be on your guard against - is that they may offer you store vouchers to replace it. This is a ploy they use to reduce costs (they obviously have a deal with the chain). If it's for somewhere that stocks Breitlings, and you simply want to replace it, fine. But you may not want to, and that's where the vouchers become an issue.
In short, you are entitled to insist on a cash refund. The insurance ombudsman has explicitly criticised insurers for paying out in tied vouchers rather than cheques, though they still do it, as presumably most people just go along with it.
[1] the Financial Services Ombudsman has ruled that:
“The option to replace jewellery is not properly exercised by offering a policyholder an authority to buy jewellery up to an agreed value at a particular jeweller’s shop. That is wrong in principle, although it seems to have become a hallowed practice. It is, in fact, a denial of true indemnity.”
In my case I therefore went back to my insurer and asked for a cheque rather than vouchers. At which point they tried to reduce the payout by about £300. At which point I pointed out [2] that it states clearly on the FOS's website @
http://www.financial-ombudsman.org.u...place-cash.htm
- that: "Policyholders should be allowed to choose where they purchase a replacement and they are entitled to a cash settlement if they cannot find an acceptable alternative. In such circumstances, we would not regard it as reasonable for the insurer to make a deduction from the cash settlement to represent any discount it would have got if the policyholder had bought a replacement from one of the insurer's nominated suppliers."
[3] There follows a list of recent cases where the FOS has upheld customer's rights to have cash settlements, for example this one:
"We told the insurer we were surprised to learn of the approach it had taken in this case. Our views on what is reasonable - where an insurer has to decide whether to repair or replace an item, or offer a cash settlement - are well-established. Indeed this topic featured in an ombudsman news article as long ago as October 2001 (issue 10). We upheld Mrs W's complaint. We told the insurer to pay her a cash settlement equal to the full cost of replacing the jewellery. We said it should not deduct the 20% discount that it could get from its preferred suppliers. We said it should also pay Mrs W a modest sum to reflect the distress and inconvenience she had been caused by its poor handling of her claim."
At which point my complaint went upstairs, the insurer back-pedalled, apologised, and issued a cheque to the value of the initial store voucher.
So, note that your insurer is [A] not allowed to insist that you take store vouchers instead of cash, and [B] not allowed to offer you less in cash than they offer in store vouchers.