This work is concerned with an analysis of Holder 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 Holder calmness assumption are analyzed. Also sufficient conditions for Holder calmness of sublevel sets and of inequality systems will be given and examined. Further, since Holder calmness of nempty 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 polymials and of general solution sets of polymial systems is investigated. The question to be answered is in which way the maximal degree of the involved polymials is connected to the exponent of Holder calmness or of the error bound for the system in question.