Can you please share a link so I can take a look?
Connections uses the same underlying tech to apply searches as WP uses for searching, So search results would be no better or worse than the core WP search.
Things you can do to tweak to get more relevant search results.
Navigate to the Connections Settings admin page and click the Search tab.
- Limit the search fields to the absolute minimum.
- Disable the LIKE option. After you do, do a test search. If you do not get results, then you need to enable the option as the WP install does not support FULLTEXT searching. FULLTEXT will generally return better results sorted by relevance as determined by the database.
Also, search will return results if the term being searched for exists within HTML tags in the bio/nots fields. You can read a more in depth explanation in regards to this in this post to another user. The short version is that this is not a Connections bug or limitation, the same occurs with core WP searches too. The reason is that there is not a way to exclude searching within HTML tags for matched terms.
Hope this helps!