What Application Performance Management (APM) certifications do exist?

Yes. DataDog comes up with Certification for Support and Implementation associates. 

There are AppDynamics certifications that are quite popular nowadays:

1. AppDynamics Certified Associate Performance Analyst

2. AppDynamics Certified Implementation Professional

Also, for Dynatrace:

Dynatrace Associate Exam – Application Monitoring Certification

Thanks,

Pradeep Singh

Each vendor will typically provide a certification for their tool.  I expect this for every vendor.  I'm not aware of a tool agnostic APM certification .... which would be an interesting cert I would love to use when evaluating candidates. 

Yes, it is CA APM has its own certification module.Likewise other product also