Migrating MySQL databases to a new server with phpMyAdmin

Looking for the best way to migrate a dozen or so MySQL databases from an old Mac mini to a new one. I've tried the source machine's phpMyAdmin (v. 4) EXPORT command, using what looked like reasonable options, and with all my existing databases selected. It created a 5+GB SQL file. Scanning through it, I see the "CREATE TABLE" commands but not any "CREATE DATABASE" commands. Am I doing it wrong?