I do like to grill shellfish, shrimp and lobster, in particular. I’ve grilled scallops as well, but find that the grilling flavors clash with the sweet delicacy of the scallops.
Shrimp and lobster, while similar, are really different beasts when they come from the grill. Shrimp generally get a little char since the flesh comes in contact with the grill (albeit briefly), which makes for just an accent note. Lobster, on the other hand, tends to be grilled in the shell, adding nuance to some of the meat.
With that in mind, I would tend to recommend different style of wines for the two. The shrimp can take on many a nice Chenin Blanc, even versions with a suggestion of sweetness. While I generally don’t like sweetness in wines with shellfish, in this case the sweet edge can parry any bitterness that arises from the grill.
The lobster, on the other hand, is all about classic pairings and I do think that Chardonnay and lobster is a classic match. Look for a Chardonnay that has some subtle wood tones, which should help form a bridge between wine and smoke-toned lobster deliciousness.
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