If the remains have been cremated, the accompanying documents should be:
Cremation certificate
Official death certificate/post mortem report
Certificate of release (transit permit)
Permit from the Health Department of the Kingston and St. Andrew Corporation or their equivalent in Montego Bay.
The remains will be examined and detained by Customs at the airport until the permit has been obtained. The permit is also obtainable prior to arrival of the human remains. Documents may be faxed to the KSAC Department (1876) 754-4483.

follow this process and u should have no worries at all. the best would be to get the permit before u travel to avoid having to leave ur loved one at the airport, taxi to get the permit, pay the fee and go back thru customs to have ur loved one returned to u (which should b a straight forward process however not all customs reps understanding of the process is the same).
when i brought my sisters' cremains on island, it was a huge emotional mashup. i did not hide her well and did not have any of the documents needed. she was confiscated and i had to go get documents,pay and return to airport customs to fight to get the cremains back..... totally out of order considering i had done what they required. not something i would want to hear of anyone having to deal with!
years later i brought part of my mothers' cremains on island with no problems. not having the JA permit and did not want to leave her at the airport and come back, i hid the cremains and walked thru customs with no problems at all.
please do keep in mind that altho some have no qualms with cremains, many jamaicas do.