Normally, to check if my server smtp connection alive, I just do telnet to port 25 from my workstation. if the smtp banner displayed, it means that the connection to the smtp server is good. I have done this for years.
$ telnet smtp.example.com 25 Trying xxx.xxx.xx.xxx... Connected to xxx.xxx.xx.x. Escape character is '^]'. 220 smtp.example.com ESMTP Postfix ehlo host.example.com 250-smtp.example.com 250-PIPELINING 250-SIZE 52428800 250-ETRN 250-STARTTLS 250-AUTH LOGIN PLAIN 250-AUTH=LOGIN PLAIN 250-ENHANCEDSTATUSCODES 250-8BITMIME 250 DSN quit 221 2.0.0 Bye Connection closed by foreign host.
Although many tools that are deliberately created for this purpose, still, I prefer just using telnet to port 25. I have made a simple perl script, with the intention that the things I do for years manually can be done automatically.