Good word for those who give out awards

Solution 1:

The question phrasing ("organizations that gave out those awards") is too muddled for a definitive answer to be given. 'Presenter' is a proper word for the person that hands over the award. 'Sponsor' is a proper word for an organization that funds an award. 'Host' is a possible word for an organization that puts on an awards ceremony.

Solution 2:

It may depend some on the type of award, but sponsor covers a lot of territory:

1. a person who vouches or is responsible for a person or thing.

Solution 3:

"Organization" works if they're all organizations. "Source" works if you want to be more general, for example if some awards are awarded by people rather than groups.

If the award context is already established (this is a list of awards, with such a heading), then you don't really need an award-specific word like "awarder" (which, as you say, isn't great).

Solution 4:

As ever, it depends on the context. In some situations, donor might be appropriate.