It's not as difficult as it sounds. I exported a mare in late September.
The first thing to make sure of it that the vet doing the health check is certified to fill out the federal form. Yes, all the requirements with CEM must be verified and travel restrictions must be met. Once you have your vet sign off on the health cert, Then you need to either send it to one of your states federal vets to endorse it Or I highly suggest that you make an appointment or have your vet make an appt. and take the certificate to your states federal vet office in person if you are able to. This way it does not get lost on someones desk and you don't end up with a certificate that is almost expired. If you take it in person, you get it back right away. It is around $100 dollars give or take, I can't remember for sure the exact amount to have them endorse it. You will get back three copies that have raised seals on them. You will need three copies of everything, sales receipt, three copies of a coggins that has been done within six months, and I also suggest three copies of their papers too. I placed a copy of each piece of paperwork in a packet, and just for safe measure incase anyone else at customs wanted copies, I made sure there was an extra two or three packets of copies of everything. Make sure you mark the packets that have the raised seal paperwork from the federal vet, those copies go to the"important" people.
Once it was explained to me that my vet would issue the health cert. and I needed to bring that to the federal vet to have it endorsed, the rest was a piece of cake. Make sure your vet has the proper clearance to issue a health cert that can be endorsed by a federal vet, otherwise the federal vet will turn you away. It happened to someone while I was in the office waiting my turn.