The magnetic properties of the triangular magnet CeMgAl${}_{11}$O${}_{19}$ were investigated by magnetization and specific heat measurements down to $T=0.03$K on single crystals grown by the floating zone method. The formation of effective spins $S_{eff}=1/2$ below $T<10$,K was confirmed both by DFT calculations and specific heat measurements. No magnetic order was found down to $T=0.03$K despite the formation of magnetic correlations observed in specific heat. The measured magnetization was compared with DMRG calculations and their agreement supports the proposal of a strongly anisotropic magnetic interaction antiferromagnetically coupling the spin components in the $ab$ plane and ferromagnetically coupling the spin component along the $c$ axis. However, our quantitative study of the magnetization places CeMgAl${}_{11}$O${}_{19}$ further from the ferromagnetic quantum critical point than inferred from the previous inelastic neutron scattering study. Finally, we suggest that the absence of magnetic order may be promoted by the structural disorder revealed by single-crystal X-ray diffraction (Ce deficiency, Mg/Al site mixing, and Al(5) splitting).