For example, if the search term is only found under a heading with an anchor or ID, the search result could link directly to that heading.
Eg: Result for query
thingamabobs could like direct to
<h3 id="section-3">Section Three</h3>
<p> This section is about thingamabobs, read on for more...</p>
If not natively supported, perhaps could it be done by processing at crawl time and treating each section as a different document?