The JOptionPane class will allow you to give any JComponent as argument
as well as which buttons and which Icon you want as argument. So in
your case, I would translate your JFrame into a JPanel, and then you
call the following (for example):

JOptionPane jOpt = new JOptionPane(yourPanel,
                           JOptionPane.QUESTION_MESSAGE,
JOptionPane.OK_CANCEL_OPTION);
JDialog dialog = jOpt.createDialog(parentPanel, "");

dialog.setVisible(true);
Object val = jOpt.getValue();
// Check for yes or no button pressed
if(val != null) {
    if(val instanceof Integer) {
        int intVal = ((Integer)val).intValue();
        if(intVal == JOptionPane.OK_OPTION) {
            // do the stuff you want to do if the user presses ok
        } else {
            // do the stuff you want to do if the user presses cancel
        }
    }
}

Kind regards, Jonck