Recent versions of the Claymore mining software prints a warning in the miner console if no API password has been specified. As long as the Claymore API port isn't exposed to the Internet, this warning can be ignored. In deployments with Awesome Miner, there is never a need to expose this port to the outside.
If you still want to configure a password for the Claymore API, it can be manually specified as a command line parameter to the miner. Open the Properties of a miner, go to the Command Line section and add the command line argument
Next, Awesome Miner must also be instructed to include the password in all API requests to the Claymore miner. Open the Options dialog, Mining Settings section and enter the same password as specified for the miner in the field for Send password for Claymore API requests.