How to easily determine, which outbound ports aren't blocked by firewall

How to easily determine, which outbound ports aren't blocked by firewall

I'm behind fairly restrictive firewall regarding ports, that can be used
for connecting outside. I'm also running service on my remote box, and I
want to connect to it.
Problem is, that I'm unable to find out which ports I can access, so I
don't know where I can bind the service. (The typical unrestricted ports
like 80 and 443 are already used on given machine).
I tried to run nmap -sS behind firewall to scan all TCP ports and
wireshark on the second machine to determine SYNs that I receive, but I
can see false positives (when I listen with netcat on given port and try
to connect, it fails).
Is there any tool that can serve my purpose?