My brother and I ran one successfully for years, curtailed only because of our schedules and other obligations. I'm subject to going on and on and on about match play, but I'll try to restrain myself to a general description of how we did it. There may be others, perhaps even better, ways.
Ours was a 1-day event with 2 divisions, Pro and Am, held on a fun but fairly short course (Earlewood). It was a single elimination bracket (like NCAA March Madness; in fact, ours was in March and also named March Madness. Clever?).
It was 18 holes for the first round, then 9-hole matches each subsequent round. 9 hole matches, with elimination on the line, are intense! 32 players per division, so that's 5 rounds.
During the 3rd & 4th rounds, everyone who was eliminated in rounds 1 & 2, which is 75% of the players, were automatically entered in a random draw doubles, stroke play, that was running simultaneously. Kind of an NIT. This was a key feature for us, because
* It guaranteed everyone at least 36 holes of play---the first 18-hold round, plus doubles, so they didn't worry about coming and getting eliminated in the first round.
* It meant everyone came off about the time the 9-hole championship round started, so they could be a gallery if they wished.
There are a lot of complicating logistics to match play that we worked out over the years. Things you never deal with in stroke play, like the absolute necessity of having an even number of players.
I love match play and applaud anyone who'll run some events. We need more!