private void Close()
{
((Popup)Parent).IsOpen = false;
}
In addition to your solution if you are using version 2.1 you can use InfoWindow control instead (sample here: http://help.arcgis.com/en/webapi/silverlight/samples/start.htm#InfoWindowSimple). To close a given instance of an InfoWindow you can set its "IsOpen" property to FALSE according to your application logic.