For cross-browser testing you can use three approaches.
1) If you have all the devices on which you want to check your website, just take these devices and check. It is possible, using the optimization of this process.
2) If you have any other questions, but need to test on a limited number of browsers and devices, it is possible to raise the emulators and just consistently go through the site in all available browsers.
3) If there is no device and you want good quality, then you should look for online services that can provide a real device with the required browsers in separate use.
1) Software for managing tests on real devices.
If the desired mobile devices are available for you, there will be a couple of tools for centralized web testing service and debugging:
http://html.adobe.com/edge/inspect/ and http://vanamco.com/ghostlab/
There is widely known dosbox and less known emulators for mobile:
To emulate Android you can use the official emulator here:
Or lightweight conditionally open emulator from Genymotion:
For IOS it’s pretty sad and has to rely on iPadian.
For Windows Phone there is an official emulator
It is not hard to guess that it is only for Windows.
It should be noted that all design emulation demands a cunning perversion and, as a rule, not amenable to at least some automation although with proper application of cunning, stubbornness and talent, you can try to cross the emulated OS and the device with the first paragraph.
It is also important that with emulation you can never be sure that the real device will work exactly as emulation.
For example, you can emulate IE 9 in IE 11, but since the emulation is via the console you will never know that the console does not exist in IE 9 and is created only upon its opening, and therefore, any of your console.log() in the absence of special measures will lead to errors and crashes scripts.
And finally, the third option:
3) Services to allow cross-browser testing.
It provides real device to test anything manually.
There are two types of free access and full paid access.
Free access to a common basis allows you to remotely use the 11-th mobile device sessions of 10 minutes.
Technically they can put anything, in fact the same works where the limit is 10 minutes. The initial set of units is basic. If you need to test mobile chrome under OS you will have to install it.
There’s a free trial period of 7 days. To use it you will have to set the “test center”. In the trial period the range of devices is comparable to free, but there are no restrictions on the length of the sessions anymore.