SIM cards don't have contacts list support though. They only have phone number list support, i.e. a very simple '1 number - 1 short name' mapping. So you won't be able to store a proper contact to a SIM card, that is, a contact where you have listed full, long name, street address, mail address, a couple of different phone numbers.

Because of this I don't try to save contacts to SIM when I change phone, instead I use e.g. bluetooth to send the full list of contacts to, say, my N800, where it will be saved as a .vcard file. Then I import that one on my new phone.