Many conventions run awards, from the monster of the Hugos to recognising the work of local volunteers. The Hugo ceremony is a big draw for many Worldcon attendees, but is exceptionally hard work, sucking in many people and lots of money.
The bigger awards have their own ceremonies, but many are just awarded as part of the Closing Ceremony. Voting can be done in advance or at-con, when the word goes out as to who is deserving of the good guy award like the Doc Weir at Eastercon, or just decided by a panel of the great and good.
3rd parties like the BSFA can sponsor awards, with a dual electorate of their members and convention attendees. Shortlists can be the basis of programme items.
If giving an award to the reticent, ensure you have dragged them to the ceremony to receive it, or have a nominated proxy. Its often kinder to pre-warn people, as not all like the limelight.