a) You could install this mod:
https://www.ubbdev.com/forums/ubbthreads.php/topics/318145/%5B7.x%5D_Google_Adsense_Search.html#Post318145

I'm not sure why it's called "Google AdSense Search", when it is actually "Google Custom Search" - But if you also have an AdSense account, you could link the two, to help monetize your forums.

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EDIT: UBBT 7.5.8 BUG! The "SEO URL upgrades" (htmlspecialchars at the end of ubbthreads.inc.php) that were added in 7.5.8 actually broke any type of SEO that UBBT URLs already had and also broke the simple copy/paste linking features. The corrected, SANITIZED URL is :
https://www.ubbdev.com/forums/ubbthreads.php/topics/318145/7-google-adsense-search.html

The fix to this UBBT 7.5.8 bug is posted HERE
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b) You could also tell your mods/users to just add an "+" to the beginning of each search term, to match ALL search words. That will dramatically improve the search results. Or edit this into your scripts\dosearch.inc.php

c) At the expense of your server's allocated memory-per-process defined in php.ini (this is 2014 and 128M or more shouldn't be a problem -- unless you're on a "thrifty" shared server) you could also edit your scripts\dosearch.inc.php MAX_SEARCH_RESULTS from 200 to 400. Or set default the "results to show per page" ($Limit) from 25 to 50... or set the default "Newer than" from "1 week" to "10 years" and just use a "display:none" css style.
READ THIS: https://www.ubbcentral.com/forums/ubbthreads.php/ubb/showflat/Number/29074 (from 2003, regarding UBBT6.4.0 w/PHP4)

There are quite a few other SIMPLE things that can be done to improve the current search code and/or the templates/default/search.tpl file.

Though, many forums replace their entire stock forum-search pages with Google Custom Search.
GCS docs can be found @ https://www.google.com/cse/docs/


Current developer of UBB.threads PHP Forum Software
Current Release: UBBT 7.7.5 // Preview: UBBT 8.0.0
isaac @ id242.com // my forum @ CelicaHobby.com