How to get a method to wait until the timer code has executed?

Question

public void highlightThisText(){

    int delay = 1000;
    ActionListener tp = new ActionListener(){

        public void actionPerformed(ActionEvent ae){
            try{
                System.out.println();
                if(name.equals("Correct")){
                    thisPanel.getHighlighter().addHighlight(startIndex, endIndex, hl);
                }
                else{
                    anotherPanel.getHighlighter().addHighlight(startIndex, endIndex, hl);
                }

            } catch (BadLocationException ex) {
                ex.printStackTrace();
            }
        }
    };
    Timer t = new Timer(delay, tp);
    t.setRepeats(false);
    t.start();      
}

I need my program to enter into the highlightThisText method, executed the timer code, and after the delay leave the method. I understand that I cannot use Thread.sleep(1000); as this will block the EDT, but I cannot find any other examples on here with a similar problem. startIndex and endIndex will be incremented after the method is left which means the the correct line will not be highlighted.

Any help will be highly appreciated.