A set S of hypersubstitutions is called an M-solidity testing system for a class of varieties if it is possible to determine all M-solid varieties in the class using only the hypersubstitutions from S. If S is a minimal such set, we will call it an M-solidity basis for the class. In this paper, we relate solidity testing systems to the Galois connection between hypersubstitutions and varieties, and present a number of examples of solidity testing systems for several different types of varieties, including examples of the existence of finite M-solidity bases for various classes.