Reduce jQuery append method
Instead of writing append two times, why don't append a single time with two different values depending on the length of searchBox?

Also, moving the trimmed search value into a variable simplifies the code a bit.

var text,
    trimmedSearch = searchBoxValue.trim();
if (searchBoxValue.length &gt; numCharToDisplay) {
    text = '&lt;div class="noresults"&gt;&lt;span&gt;Searching "' +
    trimmedSearch.substring(0, numCharToDisplay) +
    '..." Found No Results&lt;/span&gt;&lt;/div&gt;';
} else {
    text = '&lt;div class="noresults"&gt;&lt;span&gt;Searching "' +
    trimmedSearch + '" Found No Results&lt;/span&gt;&lt;/div&gt;';
}
searchDropDown.append(text);


Using ternary operators, as you suggested, wouldn't be a good practice since it complicates things up, leaving maintenance really difficult.