Delafossite compounds containing rare-earth ions have been proven to be an ideal platform to investigate frustrated magnetic ground states. Here, we discuss two triangular-lattice antiferromagnets, TlErSe${}_2$ and TlTmSe${}_2$, as potential candidates for hosting exotic quantum states. Powder X-ray diffraction data analysis of the black-color polycrystalline Tl$M$Se${}_2$ ($M$: Er and Tm) samples confirms the phase purity. Both materials crystallize in the trigonal $\alpha$-NaFeO${}_2$ structure ($R\Bar{3}m$) with lattice parameters $a$ = 4.1070(4), and $c$ = 23.1472(1), for the erbium compound and $a$ = 4.0916(1), and $c$ = 23.1483(2), for the thulium compound. Magnetic susceptibility measurements show an effective moment of ${\mu }_{\mathrm{\text{eff}}}=9.6(2){\mu }_B$/f.u. ($7.5(1){\mu }_B$/f.u.) for TlErSe${}_2$ (TlTmSe${}_2$) for temperatures above 200,K. While ${}^3$He specific-heat measurements reveal long-range magnetic order below $T_N=0.42$K for TlErSe${}_2$, no sign of long-range magnetic order was observed for TlTmSe${}_2$. Combining both experimental and computational results, we discuss the striking difference in the magnetic behavior of TlTmSe${}_2$ and map out the T-H phase diagram for polycrystalline TlErSe${}_2$.