This work proposes a constrained-optimization projection framework for preserving general physical properties in model reduction of dynamical systems. The method formulates the reduced-order model as a constrained optimization problem in which the objective function penalizes deviation from the standard Galerkin or Petrov–Galerkin projection, while constraints explicitly enforce preservation of desired physical properties (e.g., conservation laws, positivity, boundedness). This framework provides a systematic approach for structure-preserving model reduction that is applicable to a wide range of physical properties and dynamical systems.