Grazie mille,
ho provato sia Mailgun che SendGrid, ma ho un po' di problemi... in particolare su SendGrid mi da questo errore:

codice:
401 Array ( 
[0] => HTTP/1.1 401 Unauthorized 
[1] => Server: nginx 
[2] => Date: Mon, 29 Apr 2019 13:49:25 GMT 
[3] => Content-Type: application/json 
[4] => Content-Length: 88 
[5] => Connection: keep-alive 
[6] => Access-Control-Allow-Origin: https://sendgrid.api-docs.io 
[7] => Access-Control-Allow-Methods: POST 
[8] => Access-Control-Allow-Headers: Authorization, Content-Type, On-behalf-of, x-sg-elas-acl 
[9] => Access-Control-Max-Age: 600 
[10] => X-No-CORS-Reason: https://sendgrid.com/docs/Classroom/Basics/API/cors.html 
[11] => 
[12] => 
) {"errors":[{"message":"Permission denied, wrong credentials","field":null,"help":null}]}
Eppure l'API Key è giusta...