You may be able to change each entry manually to the SIM memory instead
of the phone memory on the handset. However, I find the easiest way is
to use PC software, which has the added bonus of saving all the data to
the PC in case of loss. I use LogoManager software. What phones do you
have?

Depends on the phone. Some phones have a phonebook manager and an
option that will say "Copy phonebook to SIM."

Evan