MailJet provides an mail delivery service (via SMTP or API) you can use to reliably send emails from your Newsletter plugin, monitor them, have a bounce detection and reporting service (completely integrated with Newsletter).
You can create an account on MailJet and try out the service for free (at time of writing the free account is limited to 200 emails per day).
The MailJet extension, once installed, can be configured with an API key and an API secret provided by MailJet. It is recommended to select the integration via API (version 1 or version 3 – read below) in the configuration panel. You can eventually select to integrated using MailJet as a common SMTP service, but usually it’ll be slower.
Once activated, the extension takes care to capture all generated email by Newsletter (and only by Newsletter) and send them using MailJet.
The extension schedules a daily process that checks for bounces connecting to the appropriate MailJet service. Bounced email addresses are marked as “bounced” and won’t be contacted anymore. You can check the bounce integration and see the last time it ran directly in the configuration panel.
MailJet API version 1 and version 3
Old MailJet accounts cannot use the new MailJet API (version 3) and new accounts cannot use the old version 1 API. Since there is no way to know which kind of account a customer has, once generated the API key and API secret inside the MailJet account and set them up on configuration panel, do a test using the one and the other and keep which is working for you.
New accounts can find the API key and secret at address https://app.mailjet.com/account/api_keys.