You could consider insuring the event so that the cost of the prize is covered by an insurer.
For instance, if you organised a roll a dice competition and offered, for example, a luxury holiday as a prize, then for a relatively small premium compared to the cost of the prize, the insurer would cover the cost of the holiday in the event that it is won.
The reason that the premium is relatively small is that the chance of somebody rolling all sixes, out of six or seven dice, is very low.
You could also consider asking a local business to sponsor the prize. They would benefit from the sponsorship through advertising and local press coverage in the event that the prize is won.
They could either donate the prize or you could ask them to cover the cost of the insurance premium. This means that the insurance company would pay for the holiday in the event that it is won, so the cost to the sponsoring company is less.
This method works for other competitions where the likelihood of the prize being actually won is low and the value of the prize is high. Examples include guessing a mystery number plate or a new car and hole-in-one prizes at charity golf tournaments.