When you need to apostille a Texas marriage certificate, you will need to make sure to have a certified copy of the vital record beforehand. If you need to order one, your best bet is to go through the Tennessee Department of State Health Services. Here's what their website says about obtaining one:
You must visit the county clerk's office where the marriage took place.
Texas Marriage Certificate Apostille
When you are in the United States and you need to conduct this sort of business internationally, an apostille most likely will be required. There is no margin for error with the authentication or apostille process. If mistakes are made, both your time and money will be wasted and you'll have to start all over again. If you want to look into outsourcing this service to someone with experience, please email me at firstname.lastname@example.org or call 848-467-7740 to request my services or learn more.