Apparently more than 50% of web searches now originate on mobile devices and Google recently announced that mobile-friendliness will be a ranking signal from April 21st 2015.
The best way to ensure your Joomla website search ranking is preserved is to implement a responsive template if you don't already have one.
Responsive templates are available for Joomla 2.5 and there were even a few for Joomla 1.5 but Joomla 1.5 and Joomla 2.5 are already "end-of-life" and you should ideally migrate to Joomla 3.x which ships with Bootstrap and already includes some responsive templates.
Mobile Friendly Testing and Official Instructions from Google
Google has provided a test tool at http://www.google.com/webmasters/tools/mobile-friendly/ so you can check that your website is ticking all the relevant check boxes.
For more information see: