Free tool
Mail servers look up the PTR of the sending address and then check that the name points back. A missing or mismatched reverse name is one of the most common reasons mail from a new server is refused.
What this checks
A PTR record lives in the reverse zone (in-addr.arpa or ip6.arpa) of the network that owns the address, so it is set by your hosting or access provider, not in your domain's DNS. Receiving mail servers look it up, then resolve the name they got; when that returns the same address, the reverse is "forward-confirmed". Spam filters treat a missing or unconfirmed reverse as a bad sign, and some servers reject outright.
Related tools
Servers in Luxembourg
KVM servers on our own hardware in LuxConnect DC1.1, reverse DNS from the panel, AS199839.