Neither local nor national law places time limits on burial whether the remains are embalmed or not. Although, the law states that the deceased must be buried or cremated without unreasonable delay. Usually, burial or cremation is performed within approximately 10 days of death.

When the cause of death is unknown or due to unnatural causes, a legal protection agency (the police) may, on the basis of specific indications, refer a deceased individual for forensic medical examination or investigation in order to establish the cause of his or her death. An autopsy is then performed by the regional forensic examination department of the Estonian Forensic Science Institute at Tervise 30, 13419, Tallinn, tel: +372 663 6600. After the autopsy a medical death certificate which states the cause of death is issued to the relatives of the deceased.
On the basis of the medical record the Estonian Certificate of Death is issued by the Vital Statistics Office at Pärnu mnt 67, 10135 Tallinn, tel: + 372 645 7480.

Fees include collection and transportation of remains, wooden casket, funeral home charges, administrative fees, burial costs and other services. Local burial costs roughly $1500.

There are multiple Crematoriums located in Estonia, the biggest one is in Tallinn called Tallinna Krematoorium. http://www.krematoorium.ee/tallinn/en
Mortuary firms provide assistance in preparation for burial and cremation, caskets, facilities for public viewing, containers for shipping, hearses and other transportation to cemeteries.
Mortuary fees for preparation of the body, coffin, and transportation to the crematorium are approximately $1,000. The cremation itself, in Tallinn, costs between $310-$332.

The documentation needed is a Cremation Certificate showing that the cremated remains are that of the deceased person and a death certificate. Some airlines do not allow cremated remains to be placed in checked luggage. Also, the airlines will not under any circumstance open an urn or container with cremated remains in it. Therefore, the cremated remains MUST be transported in a temporary container that can pass through TSA x-ray machines. This should be a container constructed of wood, plastic, cardboard or any non-lead based ceramic.

Options available to a family depend upon local law and practice in the foreign country. Certain documents are required by U.S. and foreign law before remains can be sent from one country to another. These requirements may vary depending on the circumstances of the death. Final preparation for shipment of remains is performed by mortuary firms, including preparation of the shipping container and delivery to the airport. Human remains transported out of Estonia must be within a coffin encased within a sealed metal container and placed in a wooden packing case adequate for overseas transport. The coffins, metal containers, and shipping cases are all available locally. They are prepared according to international regulations and meet the requirements for shipment out of country. The total cost of mortuary preparation of travel coffins and the body, and air shipment to the U.S. is approximately $5,000. There will be additional costs if remains need to be transported within country prior to their departure from the capital.

To export human remains, the following documents are required:

Official Death Certificate;
U.S. Certificate of Death.
Consular Mortuary Certificate. A U.S. consular mortuary certificate is required to ensure orderly shipment of remains and to facilitate U.S. Customs clearance. The certificate is in English and confirms essential information concerning the cause of death. The U.S. consular officer will prepare the certificate and ensure that the Estonian death certificate, affidavit of the foreign funeral director, together with the consular mortuary certificate, accompany the remains to the United States.
Affidavit of Foreign Funeral Director. The U.S. consular officer will ensure that the required affidavit is executed by the local funeral director. This affidavit attests to the fact that the casket contains only the remains of the deceased and the necessary clothing and packing materials. The affidavit may also state that the remains have been embalmed or otherwise prepared.

An application to exhume remains may be submitted to the local government authorities. In this case, applicants are responsible for paying all the fees associated with exhumation.
The disinterred remains may be sent to the U.S., taking the necessary precautions, depending on the state of the remains.