Welcome to Android Central! Which phones are these? If you're getting a new Samsung phone, use
Smart Switch.
In the future, you can avoid this hassle by saving your contacts to your Google account, instead of the local Phone account. Saving them to your Google account syncs them automatically to your Google Contacts in the cloud, which (a) keeps them safe in case something happens to the phone, and (b) syncs everything easily to a new phone.