Posted by For one of our clients I needed a landing page. This page needed to enable the user to search for site-collections. As these were to become at least 20.000 site-collections, it needed to be fast and accurate.
Now with SP2013 you can do this out of the box and easily. Just use the Search Query and Search results Web Parts.
In my case, I wanted to use the Title of the site-collection as search-base. To enable this, add the said Web Parts to the page. Edit the Search Results Web Part. In my case I used this syntax:
path:<sharepoint>/sites contentclass:STS_Site site title:{SearchBoxQuery}
This will return all site-collections which titles comply with the text in the search box.
Easy and 5 minutes of work. If you want, and are interested, you can look into this further. The Search results Web Part is a very powerful tool with a lot of options. But beware: before using these Web Parts, make sure you have Search up and running and you have at least a full index or incrementally updated one.
Have fun!
Governance, Risk, Security and Compliance 
Oh, btw. You can extent this query of course. For example: let’s search on both the site-collection name or url:
path:http://sharepoint contentclass:STS_Site (sitetitle:{SearchBoxQuery} OR sitename:{SearchBoxQuery})
Using this, you can create entire webpages builld around search. Search enabled web… Cool (at least, I think so)….