I've just taken out essential cover for a couple of spaniels, with a claims limit of £4000. I have now noticed that "Any claims that exceed the policy limit" are not covered. I asked DL what would happen if my dog was ill or injured with a bill for £5000 - and explicitly asked if they would pay £4000 and I would be liable for the additional £1000 - they simply would not answer saying it was down to their claims team to make a decision at the time. I've not made a claim and they are already 'wriggling' - I don't want to find out that they won't pay should my pet be seriously ill or injured - that is not my idea of what insurance is for