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We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles et al. (2011,<jats:italic>Econometrica<\/jats:italic>79, 1541\u20131565). Since it is impossible to have inferential methods based on the central limit theorem, we develop two alternative approaches relying on the concentration inequality and bootstrap approximations. We show that expected diameters and coverage properties of resulting sets have uniform validity over a large class of models, that is, constructed confidence sets are honest. Monte Carlo experiments illustrate that introduced confidence sets have reasonable width and coverage properties. 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