What sized frame should I buy for my 11" x 17" sized poster?

If you go to a store that sells frames, sometimes they have the matte already in them and they’ll tell you size of the frame and the size of the matte… So just find a frame+matte where the matte is reasonably close to 11×17..Unfortunately you may not find that exact size

My rule of thumb is; if the picture is say, a 5×7 then frame it in an 8×10 frame,
8×10 = 11×14,
11×14=16×20 etc.
Plus always have more matte at the bottom of the framing. It just gives a more eye adjusting perspective to the framed artwork.