yorozu

The searching is narrow down a search depends on custom field you saved. 
So, it’s basically avoid a not found. 
You’d like to use in widgets.

Search Refinement

Just another search refinement plugin depends on custom filed.

bennettmcelwee

If you have a Search box on your site, Search Meter automatically records what people are searching for — and whether they are finding what they are looking for. Search Meter’s admin interface shows you what people have been searching for in the last couple of days, and in the last week or month. It also shows you which searches have been unsuccessful. If people search your site and get no results, they’ll probably go elsewhere. With Search Meter, you’ll be able to find out what people are searching for, and give them what they want by creating new posts on those topics.
You can also show your readers what the most popular searches are. Customize your theme and add the Popular Searches block, which displays a configurable list of recent popular successful search terms on your site, with each term hyperlinked to the actual search results. You can also add a Recent Searches block, which simply displays the most recent searches. Both blocks are also available as widgets for older WordPress installations. And if you want to edit your theme, both of these functions are also available as template tags.
Search Meter installs easily and requires no configuration. Just install it, activate it, and it starts tracking your visitors’ searches.
<h4>View Statistics</h4>
To see your search statistics, Log in to WordPress Admin. On your dashboard you will see a Search Meter widget listing search statistics from the last seven days. For more details, go to the Dashboard menu on the left and click Search Meter. You’ll see the most popular searches in the last day, week and month. Click “Last 100 Searches” or “Last 500 Searches” to see lists of all recent searches. You can download the statistics as a file that you can open in Excel or a similar program.
<h4>Manage Statistics</h4>
There are a few options available if you go to the Settings section and click Search Meter. Use the radio buttons to determine who will be allowed to see the full search statistics. You can also type in a list of filter words; any search terms containing these words will not show up in the Recent Searches and Popular Searches blocks.
Advanced users: You can check the “Ignore” box to tell Search Meter to ignore searches made by logged-in administrators, so you can test things without cluttering your search statistics. You can also check the “Keep detailed information” checkbox to make Search Meter save technical information about every search (the information is taken from the HTTP headers).
Use the Reset Statistics button to clear all past search statistics; Search Meter will immediately start gathering fresh statistics.

Search Meter

Search Meter tracks what your readers are searching for on your site. View full details of recent searches or stats for the last day, week or month.

Search Refinement vs Search Meter