How to deal with certificates using Selenium?

For the Firefox, you need to set accept_untrusted_certs FirefoxProfile() option to True:

from selenium import webdriver

profile = webdriver.FirefoxProfile()
profile.accept_untrusted_certs = True

driver = webdriver.Firefox(firefox_profile=profile)
driver.get('https://cacert.org/')

driver.close()

For Chrome, you need to add --ignore-certificate-errors ChromeOptions() argument:

from selenium import webdriver

options = webdriver.ChromeOptions()
options.add_argument('ignore-certificate-errors')

driver = webdriver.Chrome(chrome_options=options)
driver.get('https://cacert.org/')

driver.close()

For the Internet Explorer, you need to set acceptSslCerts desired capability:

from selenium import webdriver

capabilities = webdriver.DesiredCapabilities().INTERNETEXPLORER
capabilities['acceptSslCerts'] = True

driver = webdriver.Ie(capabilities=capabilities)
driver.get('https://cacert.org/')

driver.close()

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Actually, according to the Desired Capabilities documentation, setting acceptSslCerts capability to True should work for all browsers since it is a generic read/write capability:

acceptSslCerts

boolean

Whether the session should accept all SSL certs by default.

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Working demo for Firefox:

>>> from selenium import webdriver

Setting acceptSslCerts to False:

>>> capabilities = webdriver.DesiredCapabilities().FIREFOX
>>> capabilities['acceptSslCerts'] = False
>>> driver = webdriver.Firefox(capabilities=capabilities)
>>> driver.get('https://cacert.org/')
>>> print(driver.title)
Untrusted Connection
>>> driver.close()

Setting acceptSslCerts to True:

>>> capabilities = webdriver.DesiredCapabilities().FIREFOX
>>> capabilities['acceptSslCerts'] = True
>>> driver = webdriver.Firefox(capabilities=capabilities)
>>> driver.get('https://cacert.org/')
>>> print(driver.title)
Welcome to CAcert.org
>>> driver.close()

For Firefox Python:

The Firefox Self-signed certificate bug has now been fixed: accept ssl cert with marionette firefox webdrive python splinter

"acceptSslCerts" should be replaced by "acceptInsecureCerts"

from selenium import webdriver
from selenium.webdriver.common.desired_capabilities import DesiredCapabilities
from selenium.webdriver.firefox.firefox_binary import FirefoxBinary

caps = DesiredCapabilities.FIREFOX.copy()
caps['acceptInsecureCerts'] = True
ff_binary = FirefoxBinary("path to the Nightly binary")

driver = webdriver.Firefox(firefox_binary=ff_binary, capabilities=caps)
driver.get("https://expired.badssl.com")

For Firefox:

ProfilesIni profile = new ProfilesIni();
FirefoxProfile myprofile = profile.getProfile("default");
myprofile.setAcceptUntrustedCertificates(true);
myprofile.setAssumeUntrustedCertificateIssuer(true);
WebDriver driver = new FirefoxDriver(myprofile);

For Chrome we can use:

DesiredCapabilities capabilities = DesiredCapabilities.chrome();
capabilities.setCapability("chrome.switches", Arrays.asList("--ignore-certificate-errors"));
driver = new ChromeDriver(capabilities);

For Internet Explorer we can use:

DesiredCapabilities capabilities = new DesiredCapabilities();
capabilities.setCapability(CapabilityType.ACCEPT_SSL_CERTS, true);      
Webdriver driver = new InternetExplorerDriver(capabilities);