It is the same situation when you perform Hajj or Umra and want to know whether it was accepted or not. Though no one can definitely claim that his Ziyarat has been accepted but there are some signs which can have some meaning. Accepted worship make us feel improvement in the state of our heart in loving, remembering and obeying Allah. If we feel more humble and more obedient to Allah (SWT), the Prophet (SAWA)and Ahlul Bat (AS) then it is a good sign.
Another sign of acceptance is feeling more willing to serve the Nobel cause of Ahlul Bayt (AS) and scarify in their way.
Another sign of acceptance is feeling more love and respect to all believers especially those who performed Ziyarat or wish to perform it.