For many bilingual users it is annoying if there isn't an article about something in Wikipedia in one language. When they quickly want to check if there is an article about it in another language, there is no simple way to jump from the "Search results" page in one language to anther language. Therefore I'd like to propose to add the "In other languages" section (as it already exists for article pages) also to the sidebar of the "Search results" page.
Topic on Project:Support desk
Tell your local community admins to edit MediaWiki:search-summary and add Interlanguage links for other languages. Then, from the sidebar, you should have links to Special:Search in other languages. Note that those links will go to special:search on that language, but it won't carry the search terms you had input here.
You can also go to other languages easily prefixing your search with the language code. For example: "de:Something" to search "Something" in the german language.