Example Nginx (> 1.9) configuration for adding cross-origin resource sharing (CORS) support to reverse proxied APIs. Handle error status (4xx, 5xx) and expose headers.

cors_support.conf

#
# CORS header support
#
# One way to use this is by placing it into a file called "cors_support.conf"
# under your Nginx configuration directory and placing the following
# statement inside your location block(s):
#
#   include cors_support.conf;
#
# A limitation to this method is that Nginx doesn't currently send headers
# specified by add_header when the backend returns a 4xx or 5xx status code.
#
# For more information on CORS, please see: http://enable-cors.org/
# Forked from this Gist: https://gist.github.com/michiel/1064640
#

# Check origin, add headers and define $test
if ($http_origin ~* '^https?://(localhost|www\.yourdomain\.com|www\.yourotherdomain\.com)$') {
        add_header 'Access-Control-Allow-Origin' "$http_origin" always;
        add_header 'Access-Control-Allow-Credentials' 'true' always;
        add_header 'Access-Control-Allow-Methods' 'GET, POST, PUT, DELETE, OPTIONS' always;
        add_header 'Access-Control-Allow-Headers' 'Accept,Authorization,Cache-Control,Content-Type,DNT,If-Modified-Since,Keep-Alive,Origin,User-Agent,X-Mx-ReqToken,X-Requested-With' always;
        # required to be able to read Authorization header in frontend
        add_header 'Access-Control-Expose-Headers' 'Authorization' always;
        
        set $test A;
}

# Update $test variable if this is a preflight request
if ($request_method = 'OPTIONS') {
        set $test "${test}B";
}

# If origin is allowed and is a preflight request, return 204
if ($test = 'AB') {
        add_header 'Access-Control-Allow-Origin' "$http_origin";
        add_header 'Access-Control-Allow-Credentials' 'true';
        add_header 'Access-Control-Allow-Methods' 'GET, POST, PUT, DELETE, OPTIONS';
        add_header 'Access-Control-Allow-Headers' 'Accept,Authorization,Cache-Control,Content-Type,DNT,If-Modified-Since,Keep-Alive,Origin,User-Agent,X-Mx-ReqToken,X-Requested-With';

        return 204;
}

⚠Please edit line 18. to avoid regex attacks. change to
if ($http_origin ~* '^https?://(localhost|www\.yourdomain\.com|www\.yourotherdomain\.com)$')

@Longwater1234 thanks for the heads up!