Thread moved. Please use the Digital Voice forum under Commercial & Professional Radio for land mobile radio technologies only. We have an HF specific category for digital signals, and where I have moved this thread. Thanks for your understanding.
When amateur radio operators want to confirm 2-way contacts with each other, it is generally done with what we call QSL cards (although there are a couple of electronic "paperless" options). More information about QSL cards can be found here: http://en.wikipedia.org/wiki/QSL
When someone wants to confirm that they have only monitored, but not participated in the conversation, or QSO as we call it, one can send an SWL card. Generally speaking, SWL cards are sent to short wave broadcast stations, but there is nothing stopping you from sending one to an amateur station.
I can not speak for all amateur radio operators, but the thing we tend to care about most is how the other station or stations we are talking to is receiving our signal. In the 17+ years I have been licensed, I have probably only received a handful of SWL cards.
I suppose what I am saying is that SWL cards in amateur radio are pretty rare and honestly, are of limited value (to me anyway).
In the "Good Old Days", a SWL would send a QSL, or reception report letter, and as mentioned, usually to a commercial station, either in the U.S. or abroad. I sent several of them when I was young, and got many replies. I don't know which excited me most, the response from a Foreign Broadcast Station, or a Ham stateside... Later when I became a Ham, I remembered the responses I got, and in turn, I responded to ALL SWL reports. I don't operate much HF now, but if there was a report sent, I would by all means reply to the person. I am afraid that in this day and age, it may not be considered by many as something they should do, as many do not return a QSL, unless it is for some hard to obtain station in a contest. Had I not been so well received, I might not have continued on with my radio hobbies.
The way to try is to copy the callsign of the station; usually one or two letters, with a number and then one to three letters behind the number. Once you have that, go to QRZ.COM Callsign Database and use their callsign lookup tool to determine their location/address. You're more likely to get a reply if you send something like a local postcard with a signal report and when you heard the transmission. A self-addressed stamped envelope would also increase your chances of a reply since hams really don't get much in return for just a "signal report" when an actual two way transmission might qualify them for a variety of awards. Good Luck!