The following procedure has been tested on OS X 10.9.2, MacTex-2013 and TextMate 1.5.11.

Install minted and its dependency (pygmentize)

sudo easy_install pip  
sudo pip2.7 install Pygmentize  
sudo tlmgr install minted  

In TextMate go to Bundles --> LatTeX --> Preferences... and fill the Option field with the following: -shell-escape.

Declare the package in your tex file:

\usepackage{minted}

Now you can do:

\begin{minted}{java}
    response.setContentType("text/plain"); 
    PrintWriter out = response.getWriter(); 
    out.println("Hello");
    out.close();
\end{minted}