There is currently no super-browser that can emulate all the quirks and issues of other main browsers.
Your simplest solution would be to actually install the browsers you find people using on your site. If you need a separate computer for all that, try asking someone who works at a big company if they have access to discarded company computers - often these make great testing platforms, routers, or servers.

For your reference
you can install multiple versions of Internet Explorer on the same computer: see this link to skyzyx.com's downloads page for more information.Remember that the annoyance users get from using outdated or broken browsers is not seeing the Web in its full glory, and this annoyance can push them towards a better browser. Consider putting a conditionally visible note on your site's main page encouraging visitors to get a
better browser.

Reply