  Entangled two-qubit states are the core building blocks for constructing
quantum communication networks. Their accurate verification is crucial to the
functioning of the networks, especially for untrusted networks. In this work we
study the self-testing of two-qubit entangled states via steering inequalities,
with robustness analysis against noise. More precisely, steering inequalities
are constructed from the tilted Clauser-Horne-Shimony-Holt inequality and its
general form, to verify the general two-qubit entangled states. The study
provides a good robustness bound, using both local extraction map and numerical
semidefinite-programming methods. In particular, optimal local extraction maps
are constructed in the analytical method, which yields the theoretical optimal
robustness bound. To further improve the robustness of one-sided self-testing,
we propose a family of three measurement settings steering inequalities. The
result shows that three-setting steering inequality demonstrates an advantage
over two-setting steering inequality on robust self-testing with noise.
Moreover, to construct a practical verification protocol, we clarify the sample
efficiency of our protocols in the one-sided device-independent scenario.
