Here is most of my golfing cigar paraphernalia I carry around in the mini golf bag: a cutter, a handful of lighters and a Cigar rest/ divot tool.
DIVPRO® - Six Tools In One! The ultimate Golf companion.
I use this mostly on the greens when I'm putting or on the tee box. I don't like to lay my cigar on the ground; mostly because I usually play early mornings when the ground is dew laden.
Like @Gunther7912 mentioned, I also use the Get a Grip Clip.
For a full round, I bring a 5-cigar Herf-a-dor and/ or a 3-cigar leather case like @WNYTONY if I'm bringing extra to dole out.
There is likely a 2-3 more cheap lighters like Ronson jet-kites or Bics throughout my bag; you can't have too many.