<form method="get" action="http://www.google.com/search">
  <input type="text" name="q" size="31" maxlength="255" value="" /> 
  <input type="hidden" name="domains" value="twiki.org" /> 
  <input type="hidden" name="sitesearch" value="twiki.org" /> 
  <input type="submit" name="btnG" value="Google Search twiki.org" />
</form>

...to get this:

Further customizations like search results within your own page template are available with free registration: http://services.google.com/cobrand/free_trial

Another idea is to combine go and search in the GoBox. See related discussions in PhotonSearch, PluggableGoBox, GoIsSearch, SearchSuggestion.

Q: Is it possible to limit the search to the [name of web] only?

stuff to get moved to another topic

TWiki tries to do both: allow using < and > characters in text and support html markup. The heuristic is:

• a pair of <, then > in one line is assumed to be a tag
• unpaired < and > are literal -- like in the Google form above!

The business about the unpaired < and > and the way you joined two lines in the bulleted list are rather subtle / interesting (look at the above two bullets in edit mode).