Place each salmon fillet skin down into a baking dish. Brush each fillet with a small amount of tamari sauce (about 1 tablespoon per each fillet). Let salmon marinate for 30 minutes. In the mean time, prepare the pasta as described below.
Preheat a gas grill.
Zucchini pasta:
Heat olive oil in a large skillet on medium-high heat. Add sliced zucchini and minced garlic and saute for about 5-7 minutes, occasionally stirring, until zucchini softens and browns a bit, uncovered. Midway through cooking, season with salt. Note: Depending on the size of your skillet, you might have to cook zucchini in 2 separate batches.
Cook pasta according to pasta instructions. Drain and rinse with cold water (to stop pasta from cooking). Add cooked pasta into the skillet with zucchini and garlic, on low heat. Add freshly shredded Parmesan cheese into the skillet and stir pasta on low heat to melt the cheese. Add salt and pepper, to taste. Cover, and remove from heat.
Grilling the salmon:
Place each salmon fillet on an individual piece of foil large enough to fold over and seal. Brush each salmon fillet with more tamari sauce. Wrap each salmon tightly into foil packets. Place the foil packets with salmon on the hot grill and cook for 10-15 minutes to reach the desired doneness.
Remove each salmon fillet from the packet and serve over pasta. If salmon is not salty enough, brush the top of each salmon with a touch of tamari sauce.