You can easily add an event search to each of the Frontend calendar views. There are two steps to add a search option.
Add the Search items to the Allowed Views in the Calendar Base's plugin (see Configure the Plugin: General Tab). There you will be offered a number of search options:
Search Event
Search Location
Search Organizer
Search All
For the main calendar page's search option, select Search Event. (See Advanced Search Options for additional search options.)