If the squid aren't pre-cleaned, separate the tentacles from the body and then remove the "beak" and other innards from inside the sac. (See Notes for details.)
Score one side of each squid body with a paring knife, taking care to cut deeply enough to open up the cavity but not to cut all the way through. (Inserting a butter knife into the cavity helps with this.)
Whisk the marinade ingredients together in a mixing bowl. Add the squid and let it marinate for at least 30 minutes.
When you are ready to cook, drain the squid well of its marinade, patting it dry.
Heat your griddle as hot as you can get it then sear the squid pieces on both sides until they have browned nicely—but take care not to overcook the squid. If the griddle is hot enough, the process shouldn't take more than 2-3 minutes per side.
Serve right away, on a bed of salmoriglio sauce, and more on the side for those who like to dip.