In this paper, a new framework to address the stability preservation problem. in projection-based model order reduction is presented. Sufficient conditions for obtaining stable reduced models are established and proven by using the notions of contractivity and matrix measure. Based on these results, we present two model reduction algorithms that preserve stability using any orthogonal projection. In addition, we show that for some system classes, stability preservation can be guaranteed just by choosing a suitable state space representation, which is applicable to the large class of models obtained by the Finite Element Method (FEM).