As of 1 July 2013, Swisscom customers can use their iPhone with any SIM. Unblock this device using the SIM unlock from Apple. You do not need to contact Swisscom. You can find details of how to unlock your iPhone at Apple(opens in new tab).
Swisscom does not guarantee that an unlocked iPhone will work perfectly with a SIM from a different mobile phone provider. Before you unlock your iPhone, find out from your new provider what services are provided for iPhone (Internet access, MMS, Visual Voicemail, tethering, etc.). Any limitations resulting from using a SIM from a different provider are not classified as device faults and are therefore not covered by the Swisscom guarantee.