Problmes when serializing Objects containing a Binary

Hello

They are. The BinaryFormatter (and other generic.NET serializers) serialize Binary objects.

However JavaScriptSerializer (and its more advanced variation from Newtonsoft) do not work with MemoryStream and any objects based on it. They do not care to serialize Stream contents and thus are useless in your case.
You need to change the data field type from Binary to Byte and then do something like

new JavaScriptSerializer().Serialize(new TPerson {
Signature = new RemObjects.SDK.Types.Binary("Bli-blah-blubb").ToArray()
});

Regards