[The Squatter of Amon Rûdh]

How about when Boromir died and they put him in a boat and sent him down a water stream, with a sword on his chest? And they recite that poem about the winds? That was reminiscent of the vikings' burial rituals. But maybe that wasn't an actual ritual?

They were a bit pressed for time to dig a grave:

'First we must tend the fallen,' said Legolas. 'We cannot leave him lying like carrion among these foul Orcs.'
'But we must be swift,' said Gimli. 'He would not wish us to linger. We must follow the Orcs, if there is hope that any of our Company are living prisoners.'
...
'Then let us do first what we must do,' said Legolas. 'We have not the time or the tools to bury our comrade fitly, or to raise a mound over him. A cairn we might build.'
'The labour would be hard and long: there are no stones that we could use nearer than the water-side,' said Gimli.
'Then let us lay him in a boat with his weapons and the weapons of his vanquished foes,' said Aragorn. 'We will send him to the Falls of Rauros and give him to Anduin. The River of Gondor will take care at least that that no evil creature dishonours his bones.'

The funeral of Boromir is, then, a hastily improvised affair. Their first choice would have been to bury him, but lacking the tools for a grave and materials for a cairn, the river was chosen to bear him away. It is very redolent of a Viking funeral, though, and perhaps this is why it seems so fitting that it should be done in this way.