In this short article the author uses Courant’s nodal domain theorem in a way similar to J. Choe [Arch. Ration. Mech. Anal. 109, 195-212 (1990; Zbl 0695.53045)], to find initial lower bounds for the index of symmetric Wente tori. He obtains as a corollary that for every natural number \(N,\) there exist only finitely many symmetric Wente tori with index less than \(N.\) He also makes use of the explicit description of such tori given by R. Walter [Geom. Dedicata 23, 187-213 (1987; Zbl 0699.53065)]. Finally, the author makes some comments about a sharp estimate and a related conjecture; a detailed description of the numerical methods to get sharper estimates of the index is postponed.