The existence of “hardest languages” in the sense of Greibach (“The hardest context-free language”, 1973) is investigated for two families of cellular automata. For one-way real-time cellular automata, also known as trellis automata, it is shown that there is no hardest language under reductions by deterministic finite transducers. For linear-time cellular automata, a hardest language under reductions by homomorphisms is constructed.