Given a Bell inequality, if its maximal quantum violation can be achieved only by a single set of measurements for each party or a single quantum state, up to local unitaries, one refers to such a phenomenon as self-testing. For instance, the maximal quantum violation of the Clauser-Horne-Shimony-Holt inequality certifies that the underlying state contains the two-qubit maximally entangled state and the measurements of one party contains a pair of anti-commuting qubit observables. As a consequence, the other party automatically verifies the set of states remotely steered, namely the "assemblage", is in the eigenstates of a pair of anti-commuting observables. It is natural to ask if the quantum violation of the Bell inequality is not maximally achieved, or if one does not care about self-testing the state or measurements, are we capable of estimating how close the underlying assemblage is to the reference one? In this work, we provide a systematic device-independent estimation by proposing a framework called "robust self-testing of steerable quantum assemblages". In particular, we consider assemblages violating several paradigmatic Bell inequalities and obtain the robust self-testing statement for each scenario. Our result is device-independent (DI), i.e., no assumption is made on the shared state and the measurement devices involved. Our work thus not only paves a way for exploring the connection between the boundary of quantum set of correlations and steerable assemblages, but also provides a useful tool in the areas of DI quantum certification. As two explicit applications, we show 1) that it can be used for an alternative proof of the protocol of DI certification of all entangled two-qubit states proposed by Bowles et al., and 2) that it can be used to verify all non-entanglement-breaking qubit channels with fewer assumptions compared with the work of Rosset et al.
 J. S. Bell, Physics Physique Fizika 1, 195 (1964).
 V. Scarani, Acta Physica Slovaca 62, 347 (2012).
 M. M. Wolf, D. Perez-Garcia, and C. Fernandez, Phys. Rev. Lett. 103, 230402 (2009).
 D. Mayers and A. Yao, Quantum Info. Comput. 4, 273 (2004).
 E. Schrödinger, Proc. Cambridge Phil. Soc. 31, 555 (1935).
 D. Cavalcanti and P. Skrzypczyk, Reports on Progress in Physics 80, 024001 (2017).
 P. Skrzypczyk, M. Navascués, and D. Cavalcanti, Phys. Rev. Lett. 112, 180404 (2014).
 M. Piani and J. Watrous, Phys. Rev. Lett. 114, 060404 (2015).
 E. Passaro, D. Cavalcanti, P. Skrzypczyk, and A. Acín, New Journal of Physics 17, 113010 (2015).
 P. Skrzypczyk and D. Cavalcanti, Phys. Rev. Lett. 120, 260401 (2018).
 M. T. Quintino, T. Vértesi, and N. Brunner, Phys. Rev. Lett. 113, 160402 (2014).
 R. Uola, T. Moroder, and O. Gühne, Phys. Rev. Lett. 113, 160403 (2014).
 R. Uola, C. Budroni, O. Gühne, and J.-P. Pellonpää, Phys. Rev. Lett. 115, 230402 (2015).
 S.-L. Chen, C. Budroni, Y.-C. Liang, and Y.-N. Chen, Phys. Rev. Lett. 116, 240401 (2016).
 J. Kaniewski, Phys. Rev. Lett. 117, 070402 (2016).
 T. H. Yang, T. Vértesi, J.-D. Bancal, V. Scarani, and M. Navascués, Phys. Rev. Lett. 113, 040401 (2014).
 M. Navascués, S. Pironio, and A. Acín, New Journal of Physics 10, 073013 (2008).
 T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, and O. Gühne, Phys. Rev. Lett. 111, 030501 (2013).
 A. Acín, S. Massar, and S. Pironio, Phys. Rev. Lett. 108, 100402 (2012).
 N. Gisin, Essays in Honour of A. Shimony, edited by W. C. Myrvold and J. Christian, The Western Ontario Series in Philosophy of Science (Springer, New York, 2009) pp. 125–140.
 J. Bowles, I. Šupić, D. Cavalcanti, and A. Acín, Phys. Rev. Lett. 121, 180503 (2018a).
 Available at https://github.com/shinliangchen/assemblage_moment_matrices.
 R. V. Nery, M. M. Taddei, P. Sahium, S. P. Walborn, L. Aolita, and G. H. Aguilar, Phys. Rev. Lett. 124, 120402 (2020).
 M. O. Renou, J. Kaniewski, and N. Brunner, Phys. Rev. Lett. 121, 250507 (2018).
 J.-D. Bancal, N. Sangouard, and P. Sekatski, Phys. Rev. Lett. 121, 250506 (2018).
 S.-L. Chen, N. Miklin, C. Budroni, and Y.-N. Chen, Phys. Rev. Research 3, 023143 (2021).
 S. Boyd and L. Vandenberghe, Convex Optimization, 1st ed. (Cambridge University Press, Cambridge, 2004).
 F. Buscemi, Phys. Rev. Lett. 108, 200401 (2012).
 M. McKague, T. H. Yang, and V. Scarani, J. Phys. A: Math. Theo. 45, 455304 (2012).
 C. Branciard, D. Rosset, Y.-C. Liang, and N. Gisin, Phys. Rev. Lett. 110, 060405 (2013).
 M. M. Wolf, Lecture Notes (2012).
 Yuan-Yuan Zhao, Huan-Yu Ku, Shin-Liang Chen, Hong-Bin Chen, Franco Nori, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo, and Yueh-Nan Chen, "Experimental demonstration of measurement-device-independent measure of quantum steering", npj Quantum Information 6, 77 (2020).
 Shin-Liang Chen, Nikolai Miklin, Costantino Budroni, and Yueh-Nan Chen, "Device-independent quantification of measurement incompatibility", Physical Review Research 3 2, 023143 (2021).
 Yi-Te Huang, Jhen-Dong Lin, Huan-Yu Ku, and Yueh-Nan Chen, "Benchmarking quantum state transfer on quantum devices", Physical Review Research 3 2, 023038 (2021).
 Shubhayan Sarkar, Debashis Saha, and Remigiusz Augusiak, "Certification of incompatible measurements using quantum steering", arXiv:2107.02937.
 Huan-Yu Ku, Josef Kadlec, Antonín Černoch, Marco Túlio Quintino, Wenbin Zhou, Karel Lemr, Neill Lambert, Adam Miranowicz, Shin-Liang Chen, Franco Nori, and Yueh-Nan Chen, "Detecting quantum non-breaking channels without entanglement", arXiv:2106.15784.
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