You could check if your server IP is on a blacklist
https://mxtoolbox.com/blacklists.aspx/ Those are usually for/against email spam. Often entries remains after the owner or the whole website changed.
If you use https you could try to find out if the user's browser doesn't support your (offered) chiphers https://www.ssllabs.com/ssltest/ Internet Explorer 6 comes to mind. We run an API and sometimes, though very rare, users try to access it using http/1.0 or other super old compiled binaries. Or see 'SSL handshake' errors in our load balancer logs.
