Plugin works well for me. I used my theme’s css to re-style the form; particularly with a background image for the text input control. But I can’t get rid of that annoying default value “Enter your search keywords here…” using style (the user needs to overtype or cut those words).
Would you consider making that configurable? I hate to create my own version of a plugin just to tweak it.

https://www.ads-software.com/extend/plugins/uw-cals-google-custom-search-engine/

Installed this, added a page for the results, linked to the CSE ID for my account and the search widget still uses the WP default search.

https://www.ads-software.com/extend/plugins/uw-cals-google-custom-search-engine/