There are ways for you to check your own firewall/router that you connect to:
This is a free service that does a quick basic scan
here is my firewall being queried:
here is also a great site which allows you to see what your own website or DNS is giving out to the world at large:
Here is the Online Port Scanner from subnetonline:
There are also many port scan response codes in case you are interested as well.
How about this site http://www.auditmypc.com/firewall-test.asp
Also how about this testing page:
Those are the 4 free scanners, and with a free scanner your mileage will vary. I added an extra one in case there were problems with one.
Did you know there are 65536 ports? the reason is that 2 bytes are used for the number of the port being used in each packet. If there are 2^16 numbers of ports(which is equal to 65536)
Not all ports are normally in use, but there are some that are not frequently used.
So if you do not do a FULL scan manually with nmap or even use a properly scripted netcat with open ports then these “automated” scans may not be worth much – but no suprise with free stuff.