You can get PC programmes that you can use IF you can connect your phones to your PC.
Otherwise, as Ratter suggests you can copy all from the old handset to the SIM card, transfer the SIM, then copy from the SIM to the new handset. It can be a bit of a pain if you have stored more info on the handset that there is room on the SIM for. You might get involved in copying bits at a time and the deleting and copying the next bit.
These days I'd not be surprised if there was a "cloud" solution somewhere, if you want to risk the world and their dog getting to your personal data.