If you don’t own the house but are a tenant, then your landlord’s homeowner insurance isn’t enough, since it only applies to the building and not to its contents. Being the case, you should buy an H04 policy to have your belongings safe under the rented house: in this way, your mobile phone can be covered.
Another possible case is that you are living in an old house and bought an H08: since the personal property coverage is more limited for this policy, you should check more carefully your insurer conditions. Mobile phones might have protection limited to fewer perils, compared to the other policies.
As for other items, if you’re covered for the loss you will pay the arranged deductible, and that will be for every time you file a claim. Not necessarily is convenient to lean on the insurance settlement, and it depends on the deductible you chose: for instance, an amount of $1,000 applied to the contents coverage refers to whatever item falls under the coverage, meaning that it might overweigh your mobile phone value, also there is the possibility you get a dissatisfactory product.
The point is: sometimes it would be better to assign the repairment to a dedicated shop or use the manufacturer warranty; theft would be another story, of course. The whole game is to choose the right coverage: on the other hand, you may decide to rise the specific limit for the cell-phone in a customized policy, if you got a pricy smartphone. Most policies have limits for every item written in the paperwork, and allow you to add things to be covered. Mind also that a claim will have an effect on the insurance premium, which you will see when renewing the policy.
Most of the insurers will compensate with a replacement model of the phone, rather than a totally new one. Of course, there are also cash limits: most of the time, they will be wide enough; if not, then you can buy a rider for your policy, which can cover the surplus.