There's roll d20 vs DC, of course, that's it. But, there's a number of ways to use that (shy of inventing your own).
le'see, dramaticized arm-wrestling could include:
Intimidate Check to 'psych out' your opponent
STR check to beat him quickly
CON check to wear him out as you struggle
Bluff check to feign weakening so he makes a final push while you're still able to handle it.
STR check to put it to bed.
By spreading it out over 5 checks, you can even out the swinginess of an opposed check, and ratchet up some drama.
OK, in a sense that's a complexity 1 skill challenge for a single character, or 3e 'complex skill check,' just using different skills, but whatever. It's shy of making up your own resolution systems, it's just applying the d20 resolution system in more detail.