I do! I use a lot of balsamic vinegar-based marinades for eggplant and portobellos, and these seem to work pretty well. I tend to use whatever I have my hand on at the moment, but generally, basil, oregano, savory, rosemary, fennel seed, or smoked paprika find their way into the marinade. So here's one recipe:
1c drained yogurt (coffee filters work great for this- drain plain yogurt for 24 hours in the fridge, in a filter-lined colander)
2tbs sweet smoked paprika
1tbs lemon juice
1 tbs sugar
1 clove minced garlic
1/4c neutral oil (canola, e.g.)
Blend marinade ingredients together and marinate portobello caps for 4-6 hours. BTW, be sure to de-stem them and spoon out the gills. The gills will turn everything black. Grill over low coals for 15 mins.
As to eggplant, I often use a glaze made from:
1/4c reduced balsamic (160oz yields about 4oz reduced- it will be very thick, and stores in the fridge for 3-4 months)
2-3 cloves crushed garlic
2tbs neutral oil
slice eggplant lengthwise, 1/2" thick and sprinkle Kosher salt on both sides of each slice- place in colander to drain for about 30-405 minutes. Rinse off under running water, pat dry, and the brush the glaze both sides. Grill over low coals (a grilling basket can help here, as the eggplant can stick and get mushy too) till done, turning once or twice.
Both work very well as the core for a sandwich. Enjoy!