As a matter of fact, iPhone won't save contacts to SIM card. However, you can utilize an Android phone to finish this task. Just follow below steps.
Step 1. Go to the Contacts app on your iPhone, find those contacts you would like to transfer to SIM card. Then tap "Share Contact" and share these contacts via email.
Step 2. Download the vCards you just shared via email on your Android phone. Go to Contacts app on Android phone, then you can choose "Import from USB storage".
Step 3. Go to Contacts app to check if contacts have already been imported to your Android phone. Then go back to "Import/Export contacts" again, this time you should tap "Export to SIM card". Of course you need to put the SIM card into the Android phone before this step.
With this way, you can copy a limited number of contacts from iPhone to SIM card. This isn't a direct and simple way to transfer iPhone contacts to SIM card. You need the extra help of an Android phone, and you also need to type emails one by one to import SIM contacts. Although, it is a good way to back up the contacts by coping them to SIM card, you can also use other backup methods to save the contacts, like use data backup programs or back up them to the cloud.
For more details, check: How to Transfer Contacts from iPhone to SIM