From a signed applet you can launch a new instance of the browser using
Runtime.exec.  This is the most robust solution and it is quite safe from
abuse since the user only agrees to accept a digital signature from a
trusted source.  We use such windows for documentation and other links for
which users click hyperlinks in applets (without destroying the applet by
launching in the same browser window).

The syntax for opening browsers is not very obvious, so here is some sample
code (where booleans such as microsoftBrowser are defined externally):

final static void showInBrowser(URL url)
{
try
{
 if (microsoftBrowser && windowsOS) Runtime.getRuntime().exec("iexplore.exe
" + url);
 else if (firefoxBrowser && windowsOS)
Runtime.getRuntime().exec("firefox.exe \"" + url + "\"");
 else if (firefoxBrowser && macOS) Runtime.getRuntime().exec(new String[]
{"open", "-a", "Firefox.app", url.toString()});
 else appletContext.showDocument(url, "_blank");
}
catch (Exception e)
{
 System.out.println("Couldn't show in browser: " + e);
}
}

Nothing is done for Safari on Macintosh since showDocument still works there
(the last time I checked).

If anyone has improvements to suggest please mention them so we can all have
a robust workaround to use for signed applets.