We explore two methods for single-crystal growth of the theoretically proposed magnetic Weyl semimetals RAlGe (R = Pr, Ce), which prove that a floating-zone technique, being both crucible- and flux-free, is crucial to obtain perfectly stoichiometric RAlGe crystals. In contrast, the crystals grown by a flux-growth technique tend to be Al-rich. We further present both structural and elemental analyses, along with bulk magnetization and electrical resistivity data on the crystals prepared by the floating-zone technique. Both systems with the intended 1:1:1 stoichiometry crystallize in the anticipated polar I4(1) md (No. 109) space group, although neither displays the theoretically expected ferromagnetic ground state. Instead PrAlGe displays a spin-glass-like transition below 16 K with an easy c axis and CeAlGe has an easy-ab-plane antiferromagnetic order below 5 K. The grown crystals provide an ideal platform for microscopic studies of the magnetic field-tunable correlation physics involving magnetism and topological Weyl nodes.