Boris Kuzmanov

This plugin lets you remove menu items with drag & drop. It basically simplifies the process of deleting the menus which can be really time consuming if you have a lot of menus. sTRASHo is located in your Appearance > Menus menu.
https://www.youtube.com/watch?v=swz5INhnDr4

sTRASHo

sTRASHo is a smart and easy way to delete your menu items.

joe_bopper

Adds search box as a choice of item in navigation menus admin area.
Features include:
<ul>
<li>now compatible with the WordPress appearance customizer,</li>
<li>search box available as a choice in the admin area for navigation menus,</li>
<li>as many boxes can be added to a nav menu as one likes,</li>
<li>search boxes can be added as children of other menu items (useful for, e.g., mega-menus),</li>
<li>capacity to change button text, placeholder and css classes from the admin area to each search box,</li>
<li>hooks to modify output (see FAQ and/or code comments),</li>
<li>very lightweight,</li>
<li>in keeping styles, html, behaviour, etc., with wordpress defaults,</li>
<li>works straight out of the box, no configuration needed.</li>
</ul>
<h4>Those wanting to translate this plugin, please do.</h4>
I believe the plugin is in a translatable state and I’ll do everything I can to help in translation. It should be relatively quick as there isn’t much text to the plugin.

Bop Search Box Item Type For Nav Menus

I like the way it behaves like any menu item so you can position and decorate it how you want. Thanks to Joe for putting me right on how to get at the placeholder text.

Nice Plugin

Adds search box as a choice of item in navigation menus admin area.

sTRASHo vs Bop Search Box Item Type For Nav Menus