For the results page to be labeled as secure by a browser, you will need to make sure that all hard-coded links in your search results Template File (or Head/Tail files) use HTTPS. Also, if you specify a BASE URL in your Template File, make sure it also uses HTTPS. You can find more information about search Template Files in the Search Guide.
The search results generated by the search engine contain links back to your website based on the search query. Those links match the documents discovered by the search spider during indexing. They are controlled by the Include List associated with the search index. Use the HTTPS protocol for all URLs in the Include List to make the links in the search results secure. (The Include List is set on the Search Configuration page at Blossom.com in the Search Engine Settings section.) If you do change your Include List to use HTTPS, you should also trigger a reindexing to flush documents retrieved via HTTP.
If you need help, send email to Blossom Support.