Unfortunately 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 according to a forum at Verizon Wireless Community, if you're under Verizon and 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.
Of interest, now you can have a spam filter on your home phone as the new website Nomorobo offers a simple and free way to block those annoying – and often illegal – automated phone calls that interrupt your day. It is a cloud-based solution that uses the "simultaneous ring" service (provided by some phone carriers) that allows numerous phone lines with the same number to ring at the same time. Find out more at CNBC.