A person that advertises that they are a "certified" mediator in the State of Texas means that they have completed the basic 40 hour mediation training. As far as I can determine, and I've asked many people to answer this question for me, apparently it means nothing in the State of Texas.
Technically when I completed my basic training in 2004 I was a "certified" mediator.
Since my basic training I have taken advanced training every year - in both family law and in mediation.
For example, in the past year I have completed approximately 100 hours of State of Texas continuing legal education in family law, mediation training and mediation teaching.
The only group in Texas that offers any sort of credentialing is the Texas Mediator Credentialing Association. I have been a credentialed mediator since 2008. In 2012, I became a credentialed advanced mediator. In 2015, I became a distinguished credentialed mediator.
There is no licensing of mediators in the State of Texas. The TMCA is the only organization that offers any sort of "title" for a mediator.
I would be wary of anyone claiming to be a "certified" mediator. Ask them what makes them a "certified" mediator. Ask them if they are credentialed by the TMCA -- very few mediators are able to qualify and maintain their membership in this organization. Ask them how many hours they have in mediation training.
Quite frankly, I've lost count of all my mediation training hours. I did quick calculation and it is easily over 250 hours just in mediation training. This does not include the hours I've spent training new mediators or the hours I've spend in family law continuing legal education.