I've seen a few different ways of deciding.
1. The higher place team gets the prize.
2. Use rock-paper-scissors to decide.
3. If only one of the tied teams has attended the presentation, give them the trophy.
4. The organisers just announce the winner based on their own opinions
5. Let the team that was mistakenly already given the trophy keep it (don't ask).
In general, I think it's okay to leave the spirit award as a tie. If there is a token prize that can't be easily split between two teams, methods 2 or 3 are fine for deciding who to give it to.
In the case where it's a decent trophy for an important tournament, I can see the merit of having a well-known convention to decide it. Method 1 does fit the bill. Everyone knows what to expect, even if it is a little arbitrary.
Presumably, the theory behind method 1 is that it's more difficult to be spirited and good at the sport than to be a spirited loser. I would think there'd be more of an argument to be made for it being more difficult to keep good spirit in close games over blow-outs, rather than just finishing position. But working that out could be too much trouble between a final and a presentation.
And of course some teams give high scores willy-nilly while other teams only give low scores. Calculating which of the tied teams played those teams that were stingy with spirit scores could be the most accurate method.
I hear recently this call was made based on the team with the better single game spirit score. Or possibly it was the opposite; the team with the more consistent spirit scores. I think there are arguments for either but neither are great arguments.
There are so many variables at work, all at the mercy of the subjective judgements of teams filling out a spirit score sheet that it would be difficult, based on some factor or other, to say for sure that one team is slightly more spirited. Its probably best to just stick with the most straight-forward 'higher placed team gets the trophy' convention.
Any thoughts?