The goal of this article is to obtain observability estimates for Schrödinger equations in the plane R 2. More precisely, considering a 2πZ 2-periodic potential V ∈ L ∞ (R 2), we prove that the evolution equation i∂tu = −∆u + V (x)u, is observable from any 2πZ 2-periodic measurable set, in any small time T > 0. We then extend Taüffer's recent result [Täu22] in the two-dimensional case to less regular observable sets and general bounded periodic potentials. The methodology of the proof is based on the use of the Floquet-Bloch transform, Strichartz estimates and semiclassical defect measures for the obtention of observability inequalities for a family of Schrödinger equations posed on the torus R 2 /2πZ 2 .