But, you say, swordfish do have scales?

Yes, they have scales, but not the type of scales that make a fish kosher. The biblical term translated as “scales” is kaskeses. This refers to scales that can be removed from the fish without tearing the skin. Scales that are one with the fish and cannot be removed without tearing the skin are not called kaskeses. Fish with such scales are not kosher. The swordfish is one of them.¹

Sorry.

Incidentally, fish that shed their scales when netted, like mackerel, are kosher. Also, any fish that has scales has fins.

Scales that are one with the fish and cannot be removed without tearing the skin are not called kaskeses. Fish with such scales are not kosher. The swordfish is one of them.

If you want to get technical, read on. I found this at koshersupermarket.com:

“Ichthyologists recognize four types of fish scale. The kosher variety of scales are cycloid(round) and ctenoid(comblike). The ganoid scale found on sturgeon, or the placoid scale of the shark are specifically excluded from the Biblical term kaskeses since they are not "removable" scales without tearing the skin from the flesh. Even an educated layman would not see any similarity between the heavy bony plates of the sturgeon or the needle-like projections on the shark skin and the classic kosher scale of the whitefish or carp.

In Fishery leaflet #531, U.S. Dept. of Interior, Fish & Wildlife Service, Bureau of Commercial Fisheries, Wash.D.C., it states "swordfish during early juvenile stage of life (up to 8 inches long), have "scales" that are markedly specialized and rather unique. They are in the form of bony tubercules or expanded compressed platelike bodies. These scales are rough, having spinous projections at the surface and they do not overlap one another as the scales in most fish do. With growth the scales disappear and the adult fish including those sold commercially have no scales."