If you have stored your supernumerary embryos by freezing them, and want to do an embryo transfer in our clinic (because our success rates are so high and we charge much less than US clinics do ), then it's possible for you to do so !
Embryos are frozen in liquid nitrogen, and you can transport them from anywhere in the world to our clinic using a dry shipper. The important thing is that the cold chain needs to be maintained, so that they remain cold all the time. You can read more about dry shippers here.
You will need to authorise your clinic to ship your embryos; and request them to do so in writing. Most clinics will lend you a dry shipper; which you will need to return to them. They will charge the dry shipper with liquid nitrogen; load your embryos in them; and then hand this over to you. You can hand carry this. The embryos are safe in the dry shipper for over 7 days. You will also need to get permission from the ICMR and we can help you with this.
There are no problems with taking the dry shipper through customs or through security, as long as your paperwork is in order; and specifies that these are frozen human embryos being used for your medical treatment; and that they are non-hazaradous and non-infectious.
If you don't want to do this yourself, you can contact courier companies who can do this for you.
These include: http://www.ivfcouriers.com/
Have your clinic provide detailed documentation about your embryos !