By default JxBrowser allows loading HTTPS web sites with invalid SSL certificates. If you need to change this default behavior and don't allow invalid SSL certificates, you can register your own LoadHandler implementation where you decide whether invalid SSL certificates should be ignored or not. For example: 

browser.setLoadHandler(new DefaultLoadHandler() {
    @Override
    public boolean onCertificateError(CertificateErrorParams params) {
        // Return false to ignore certificate error.
        return false;
    }
});

The CertificateErrorParams parameter provides information about invalid SSL certificate. You can decide whether certificate is allowed or not using its details.

import com.teamdev.jxbrowser.chromium.Browser;
import com.teamdev.jxbrowser.chromium.Certificate;
import com.teamdev.jxbrowser.chromium.CertificateErrorParams;
import com.teamdev.jxbrowser.chromium.DefaultLoadHandler;
import com.teamdev.jxbrowser.chromium.swing.BrowserView;

import javax.swing.*;
import java.awt.*;

/**
 * Demonstrates how to handle SSL certificate errors.
 */
public class CertificateErrorSample {
    public static void main(String[] args) {
        Browser browser = new Browser();
        BrowserView browserView = new BrowserView(browser);

        JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
        frame.add(browserView, BorderLayout.CENTER);
        frame.setSize(700, 500);
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);

        browser.setLoadHandler(new DefaultLoadHandler() {
            @Override
            public boolean onCertificateError(CertificateErrorParams params) {
                Certificate certificate = params.getCertificate();
                System.out.println("subjectName = " + certificate.getSubjectName());
                System.out.println("issuerName = " + certificate.getIssuerName());
                System.out.println("hasExpired = " + certificate.hasExpired());
                System.out.println("errorCode = " + params.getCertificateError());
                // Return false to ignore certificate error.
                return false;
            }
        });
        browser.loadURL("<https-url-with-invalid-ssl-certificate>");
    }
}