Although I use interlocking foam "play mats" when blocking smaller items, like the individual pieces of a sweater, for larger items like this shawl I use foam insulation board. (For REALLY large shawls I lay a sheet on a carpeted floor.)
The Swallowtail Shawl is a great one for using blocking wires. My blocking wires are 36" tig welding rods, much cheaper than "real" blocking wires. I placed one wire down the center back and two across the top edge. I made sure those wires remained straight, but allowed the wires threaded through the lower, pointed edging to curve out slightly while I pinned.
Pictures of the finished shawl tomorrow.