Steve Johnson, chef-owner of The Blue Room in Cambridge, Massachusetts, advises that a clean grill is the first step to grilling fish without having it stick. Brush on a little oil and start grilling with the skin side down. The skin adds an extra layer of protection, and it can be peeled off later if you’re not interested in eating it.Steve Johnson, chef-owner of The Blue Room in Cambridge, Massachusetts, advises that a clean grill is the first step to grilling fish without having it stick. Brush on a little oil and start grilling with the skin side down. The skin adds an extra layer of protection, and it can be peeled off later if you’re not interested in eating it.