Similar to Google Site search, but with StartPage
you'll get a better level of privacy instead. You can search the current website you are viewing for a specific word or phrase and get the results in a new tab.
Once installed you will find the "Search This Site with StartPage" button in the bottom right of your addon bar. If you do not see this please ensure View >> Toolbars >> Add-on Bar (Ctrl+/) is enabled.
This project is open-source and made with Mozilla Addon-Builder. Check it out for yourself!