The Roman Catholic Church opposes cremation, but the Boston diocese said that there would be no objection in this case: environmental regulations stipulate that only ashes may be scattered in sea burials.
There were hints, too, that the Bessette family may have taken longer to agree to this method of farewell than the Kennedys.
It was only just before the ceremony that it was confirmed that the urns containing their ashes were also on board the destroyer USS Briscoe and that they had been included in the Defence Secretary sanction for burial at sea. The Pentagon had to reissue its original statement to include their names.
Senator Edward Kennedy and two of his sons witnessed the recovery operation and accompanied the bodies back to land for the obligatory post mortems. The bodies were released to the families for cremation on Wednesday evening.
The Defence Secretary, William Cohen, simultaneously agreed to the families' request for a burial at sea, and the arrangements were finalised in a matter of hours.
Criticism of the scale and cost of the recovery operation had prompted President Bill Clinton to explain the decision as his own, taken "because of role of the Kennedy family in our national life and because of the enormous losses they have sustained in our lifetimes".
"If anyone believes that was wrong,' Mr Clinton told reporters in Washington on Wednesday, "the coast guard is not at fault, I am."
The Clintons are to attend a private memorial service in Manhattan today at the church of St Thomas More, where Mr Kennedy's mother, Jackie Kennedy Onassis, was a regular worshipper.
A second service, at the Episcopalian church in Greenwich, Connecticut - also private - is to be held for the Bessette sisters tomorrow night. A public memorial service was to be held in Manhattan last night, arranged by friends and colleagues of the deceased.
An inquiry into the cause of last Friday's crash has been initiated by the National Transportation and Safety Board and is expected to take up to nine months. One early theory is that Mr Kennedy, who had held his pilot's licence only 14 months, became disorientated in the combination of haze and half-light at the time.