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()