  We explore two methods for single crystal growth of the theoretically
proposed magnetic Weyl semimetals $R$AlGe ($R$ = Pr,Ce), which prove that a
floating zone technique, being both crucible- and flux-free, is crucial to
obtain perfectly stoichiometric $R$AlGe crystals. In contrast, the crystals
grown by a flux growth technique tend to be Al-rich. We further present both
structural and elemental analysis, 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.
