Solid fuel does make sense for a top stage, a so-called kick stage, the most notable example being the Star family. A kick stage has only smaller or similar gross mass as the payload it propels, which means that the weight savings from a high-ISP fuel are limited – you're in either case only getting a small bit of extra Δv. In other words, you're within in the nearly-linear range of the Tsiolkovsky equation. By “nearly linear” I'm referring to $e^x \approx 1+x$ for sufficiently small $x$. The infamous “tyranny of the rocket equation” only strikes when $x$ approaches 1 or larger, in this case meaning $\Delta v\gtrsim v_0$.
Thus for a kick stage, the ISP is not quite as important anymore. You might still theoretically get a better payload/fuel ratio with a good liquid stage, but only linearly better, so the simplicity of a solid design can make up for its ISP disadvantage.
This logic does however not really apply to the Antares, with (if I read the numbers correctly) the Castor 30 having a gross mass 26 t to get 6 t to LEO. So the real reason is likely corporate politics rather than engineering: as CBHacking pointed out in the comments, Orbital ATK is a company focused on solids, so they can leverage a lot of expertise there that made it more economic for them to have a solid second stage.
Sure enough, the Antares often uses also a Star kick stage. Curiously enough they also have a liquid kick stage (BTS) available – that's really a strange combination then, solid only in the second stage where it makes least sense in principle.