I don't know of any certification body that produces/ensures quality trainers.
I, as a fitness trainer for 25 years, believe that experience and time and empathy for a client give a lot more.
That said: ACE, ACSM, NPTI & NSCM all provide nationally recognized certifications that are recognized by gym chains everywhere.
Each of the above certifications provide a slightly different approach to certification, often contradicting each other.
ACE and ACSM (and, most likely, some of the others listed and not listed) are legally defensible, which means: if there is a law suit against the trainer, and he/she has adhered to the certifcation guidelines, then that individual will be supported in court.
I am ACE certified.ACE, formally a minor written exam, has now, 15 years later, turned into a comprehensive written and practical exam.
It's goal for the fitness trainer to learn is 'Do No Harm' and errs on the side of conservative training. Other exams are geared differently.
Like Physicians, fitness trainers have specialties...are you thinking of taking a certification or want to hire a trainer?