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This paper investigates constrained semi-autonomous robotic swarms in the presence of inter-robot communication delays. The objective is that all robots converge to the optimal point related to the reference given by a human operator without violating the constraints. In the presence of constraints, directly applying the human reference may make the system violate constraints. We thus apply a reference governor which suitably modifies the reference to avoid constraint violations. Due to the limited access of global information, we present a passivity-based distributed reference governor scheme. However, the presence of the communication delays could cause instability of the system. To integrate communication delays into the passivity paradigm, a passivation technique using the scattering transformation is implemented in the communication path. Based on passivity theory, we prove the convergence of the estimated states of the reference governor to the optimal solution. The simulations and experiments demonstrate the effectiveness of the proposed solution.