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I have a Google Custom Search Engine that is hosted on my website that searches a few websites that are similar to mine. When people use the search engine, I don't want them to leave my website by clicking on the external links. Can anyone help me with this? Is there some way to do this with a IFrame? I'm new to web design so thanks in advance.
You may not in any way frame or cache the Results produced by Google, except as otherwise agreed to between You and Google.
So if you really want to do this, you probably need a special exception/permission from Google. Also, before you approach Google, think through why you want to have a CSE at all -- if you also want to keep the users on your website. Those two goals are opposed to each other, IMO.
I am using the cse to keep the visitor on my group of sites. I figure if they don't find what they want and do a search then they may find it on another of my sites.
You can also prioritise the results so if you have a reasonably large site your pages should appear in the first results so you won't lose many visitors.