If your mobile phone gets stolen, your first move should be to phone your Mobile Service Provider (e.g. Vodacom, Cell C, MTN or 8ta) in order to block your SIM card so that the thieves can’t make money off your account.
A second thing to do is actually get the service provider to block your handset, which renders the phone pretty much useless, even if the thief swaps out the SIM. To do this, you need to give them your handset’s unique serial number (known as your IMEI code), which you can retrieve from your phone by dialling *#06#** on most models.
Write this 15-digit code down and keep it safe.
If thieves can’t use or sell off stolen phones, then perhaps they won’t bother stealing phones in future? (Worth a shot anyway)