This work is concerned with an analysis of Hölder calmness, a stability property derived from the concept of calmness. On the basis of characterizations for sublevel sets, procedures to determine points in such sets under a Hölder calmness assumption are analyzed. Also sufficient conditions for Hölder calmness of sublevel sets and of inequality systems will be given and examined. Further, since Hölder calmness of nonempty solution sets of finite inequality systems may be described in terms of error bounds, the local propositions are amplified to global ones. As an application the case of sublevel sets of polynomials and of general solution sets of polynomial systems is investigated. The question to be answered is in which way the maximal degree of the involved polynomials is connected to the exponent of Hölder calmness or of the error bound for the system in question.