I've been using http://www.canyouseeme.org/ for this purpose. It does have the limitation that it only allows testing the ports of the connecting IP.
Google for "scan ports" and you'll discover plenty of people offering this service already.
Knock on someone's door? Once is fine, more than about 20 times [in a day] is likely to be seen as a nuisance. You'd have some sort of exclusion order long before you get to 2^16 times.