The best thing to do if the phone is lost is to lock it remotely from the relevant "find my phone" web service - Google for Android, Apple for iPhone. You can set a custom lock screen with contact number. Only a determined thief would get past that.
I went a stage further and remotely wiped the device. I since learned that (on Android) this essentially cleans the phone up nicely for anyone that finds (or has) it. If you do that you should make sure the SIM is disabled first - reason being, if an honest person finds it (as in my case) it won't have internet access when they turn it on so it won't wipe itself and they will still be able to access your contacts - if a dishonest person has it, they'll either factory reset it themselves or it'll do that itself once they connect it to the internet, in general they won't get sensitive info (certainly no access to bank account data) without internet access. However, Hail0 used to store readily accessible links to all our data on our phones, including photo, name, address, bank account number, sort code, copies of licences, etc, etc... I don't know if mytaxi still does that.
It all gets quite complex here but the phone (Samsung Galaxy Note 4) appeared to be switched off when I collected it (no breathing light) then appeared to switch itself back on as soon as it got in range of my WIFI (which it obviously had access to) and displayed the Samsung logo until it was done wiping itself and then went straight to a setup menu starting with the option to change language from Chinese. Now its gets stranger - I've previously factory reset cheap Chinese phones and a few screens into the setup process they insist on logging on with a Google account previously associated with the phone to proceed. The expensive Samsung didn't give a fuck, it was open for any user to set up.
Half the answer might be to use a cheap Chinese phone to minimise financial loss if it's stolen. That's all I would buy myself, I only have the Samsung 'cos the older young lad upgraded to something better/newer/more fashionable and my las Chinese one had a fall from which it never fully recovered - the botton quarter of the screen no longer responds to touch!
In fact, I ordered a Cubot Max on Amazon yesterday (c.€130)... managed to cancel it when I learned that the Samsung had been found alive and well.