One option is to open a new (blank) window, maybe with javascript. Close current window and switch to newly opened window to resume testing the remember me functionality. If you close browser session (by closing the one and only window) then you may have problems when starting next browser session to resume testing the remember me functionality.
Testing the functionality may vary depending on the browser used. If Firefox (and Chrome), you get clean sessions each time, so you would have to save the remember me cookie to file/disk before closing browser session then when open new session, manually add/create back the cookie in browser session by fetching it from file/disk using Selenium API to add the cookie (but you'd probably have to do this at the target site/domain and then do page refresh after adding cookie to continue).
If testing on browsers like IE and Safari, unless things have changed, the cookie session may still be in cache. I believe these browsers don't specifically give you a clean session by default unless you request it during driver startup from the DesiredCapabilities.