Depends on what Smartphone ye've bought. iPhones (if stolen) can and are blocked completely by the network so they can't be used whatsoever. Still an expensive item to replace though.
I watched an article on the BBC the other day about how insurers manage to wiggle their way out of paying for claims though. One householder, had a house insurance claim refused , because they hadn't re-grouted the bathroom tiles every year. (think they'd had a water leak and it had flooded downstairs)
So whatever you decide to do, read the bloody small print... A mate o mine had his smartphone stolen as he answered a call. Someone ran up from behind and snatched it oot of his hand. The insurance company refused to pay out stating he hadn't protected the phone whilst using it. (WTF,,, Is there a different way of answering a mobile phone call , apart from holding it up to your bloody ear ? )