The JSP is the wrong place for this. You need to create a standalone class which does the JDBC job and let each of the methods throw an exception whenever the SQL stuff fails. 
Here's an example of a "DAO" class which does all the JDBC stuff on the User table:
public class UserDAO {
    public User find(String username, String password) throws SQLException {
        // ...
    }
    public void save(User user) throws SQLException {
        // ...
    }
    public void delete(User user) throws SQLException {
        // ...
    }
}
Then, create a servlet which uses this class and handles the exception. Here's an example of a LoginServlet:
@WebServlet(urlPatterns={"/login"})
public class LoginServlet extends HttpServlet {
    @Override
    protected void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
        String username = request.getParameter("username");
        String password = request.getParameter("password");
        UserDAO userDAO = new UserDAO();
        try {
            User user = userDAO.find(username, password);
            if (user != null) {
                request.getSession().setAttribute("user", user); // Login.
                response.sendRedirect("userhome");
            } else {
                request.setAttribute("message", "Unknown login, try again"); // Set error message.
                request.getRequestDispatcher("/WEB-INF/login.jsp").forward(request, response); // Redisplay form with error.
            }
        } catch (SQLException e) {
            throw new ServletException("Fatal database failure", e); // <-- Here
        }
    }
}
Let JSP submit to this servlet
<form action="login" method="post">
    <input type="text" name="username" />
    <input type="password" name="password" />
    <input type="submit" />
    ${message}
</form>
You see, when the DAO class throws an SQLException, the servlet rethrows it as ServletException. It will by default end up in a container-default HTTP 500 error page. You can if necessary customize this with a JSP in your own look'n'feel as follows
<error-page>
    <error-code>500</error-code>
    <location>/error.jsp</location>
</error-page>
See also: