If you are sending batches of hundreds of emails at a time, you can improve performance slightly by reusing a single HTTP connection to your ESP's API, rather than creating (and tearing down) a new connection for each message.
Most Anymail EmailBackends automatically reuse their HTTP connections when used with Django's batch-sending functions ~django.core.mail.send_mass_mail or connection.send_messages. See django:topics-sending-multiple-emails in the Django docs for more info and an example.
If you need even more performance, you may want to consider your ESP's batch-sending features. When supported by your ESP, Anymail can send multiple messages with a single API call. See batch-send for details, and be sure to check the ESP-specific info <supported-esps> because batch sending capabilities vary significantly between ESPs.