Hi N.-
My son, now 3-years old, used to do the same thing (and very occasionally still does).
There are some flaws with this approach, but it works for us: We give him 2 choices when he does this. He can eat his dinner, or we can end dinner, but there isn't going to be another meal later- this is it. If he chooses not to eat any more he gets to look at books or play quietly on or near the sofa while we finish our meal. We keep an eye on him (of course) but he isn't rewarded with mom or dad as a playmate, which is frequently what he's after
On the occasions that he chooses not to eat I include a piece of plain toast or something equally bland/uninteresting with his milk at story time. That way hunger pangs don't keep him up all night, but he doesn't feel like he's gotten a preferred/alternative meal. I also make sure that there's a decent amount of time in between dinner time and story/milk/toast. With the time gone between dinner and story time and the fact that a piece of toast isn't very similar to a typical meal, hopefully he doesn't perceive this as an alternative meal.
The "right" way to do this, of course, is to let them go without a meal so that they learn that it's in their interest to eat what's put in front of them...My son's so stubborn that doing that would be perceived as a challenge and he'd up the ante on the dinnertime tantrums. Then also there's an element of laziness involved on my part; if he doesn't eat and he goes to bed hungry he won't actually sleep for any real amount of time, which means that I don't get to sleep, either. I'm still making up for the sleepless nights when he was an infant; I like sleep. Thus the piece of toast with the storytime milk.
In any case, this approach works in my house- the tantrum ends quickly, one way or another.
Hope that this helps- Good luck!
M.