Generally, there's no way or indication saying that your message has been blocked as it will just show as sent however the other party just won't get it.
But there's an exception for iPhone users. There is a way to tell if someone has blocked your phone number on their iPhone. Find out how by checking on the links below:
And, if you're with Verizon, a forum at Verizon Wireless Community, says that if your text is blocked, you will get a text back stating that it was blocked or that the user has privacy settings on.
Verizon has this feature called "Spam Control" which enables their customers to block unwanted calls and messages.
It is a free feature to block certain phone numbers and Internet addresses from contacting you. This call & message blocking allows you to choose and block up to five phone numbers from sending text or multimedia messages to you.
Blocking will expire 90 days from the date of the first block and you just have to reestablish blocking by adding blocking preferences after they expire.