I second the recommendation for Lukas Volger's Veggie Burgers Every Which Way. I've been working my way through it and have made several of the recipes so far, all of which have been good. However, I would say that not all of the recipes in the book work well for the grill.
I've been doing everything vegan from the Volger book with mixed results. Many of the recipes use eggs, but you can do them with just breadcrumbs and water as the binder. They come out pretty delicate that way and are better in a skillet and then baked, as Volger recommends. His tofu and chard burgers use some tofu that has been browned then pureed as binder. This works ok, but the burgers came out quite delicate (but still delicious).
Silken tofu pureed in the food processor gets a thick, creamy texture that could also be used as a binder.
Eggs are by far the most common binder as they may be the best edible binder there is, since they are basically liquid protein, but obviously not vegan.
For delicate burgers, I use this cooking grid on the grill, which works great. You can find something similar at most kitchen stores.
Another binder option is steamed rice, prepared like you would for sushi. It gets sticky and makes a great binder, though they'll still be a bit delicate. I've been making the beet, brown rice and black bean burger recipe from Volger's book. I add bbq sauce and a paste of pureed rehydrated prunes, similar to the veggie burger at Hillstone/Houston's restaurant and they come out really great. They work fine right on the grill, though refrigerating them overnight makes them a little sturdier.
Another option is adding vital wheat gluten and water, aka raw seitan dough. This is what is done in the Veganomicon black bean burger recipe. I tried these straight on the grill also and they stayed together perfectly, as well as any commercial veggie burger. However, they were a little bland and could use some more seasoning.
I haven't tried any of these in burgers, but some common binders in vegan baking are peanut butter, apple sauce and Ener-g egg replacer. I bet peanut butter would work well in a burger with flavors that work with peanut, like Thai flavors or chipotle.
Falafel-style burgers also don't need any binders, they stick together pretty well and can be grilled, though you may want to use a grill grid or something similar.
Lastly, you can put a cast iron skillet or pizza stone on the grill - it's common now for grilled pizza and will work for delicate burgers.
As eggs are a very versatile ingredient: when substituting, it is important to determine whether the eggs are being used as a leavening agent or binder (or both). In recipes where the egg is used primarily as a leavening agent, I have used a mixture of baking powder (not soda), water, and vegetable oil in a 2:3:3 ratio, though you may want to experiment with the proportions depending upon your recipe. You may also need to vary the amount of other liquid in the recipe.
Where the egg is used primarily as a binder, you could use banana, applesauce, or gelatin, depending upon the recipe (obviously, you'll probably want to avoid the fruits in a savory recipe). I've used, and been thoroughly disappointed with, the available commercial "egg replacers" and don't recommend them for any purpose. I've heard of using flax, but have no personal experience with it.
However: as the father of (and resident chef for) a young child with egg and milk allergy, it is my experience that successfully substituting for eggs is very difficult. For breads in particular, I don't even bother with recipes that call for eggs or milk, and favor those that use the basic 3 (4): flour, water, yeast (salt).
Best Answer
I'd say the matzah meal is the equivalent of finer grain breadcrumbs. So what ever ratio you would usually use for breadcrumbs + eggs I'd do the same for matzah meal.