You can use digest authentication with the username and password that you use to access Wowza Streaming Engine Manager.
https://www.wowza.com/docs/how-to-query-wowza-rest-api#querycurl
For example if I want to query Wowza Streaming Engine to find information on an incoming stream I can use the following:
curl --digest -u "username:password" http://localhost:8087/v2/servers/_defaultServer_/vhosts/_defaultVHost_/applications/live/instances/_definst_/incomingstreams/myStream
That will provide information on the status the “myStream” feed heading into the default live application. If the live feed is not running then you will receive the following:
<?xml version="1.0" encoding="UTF-8" standalone="no"?><error><wowzaServer>4.7.1</wowzaServer><code>404</code><message>The server has not found anything matching the request URI</message></error>