The millimeter wave (mmWave) bands offer the possibility of orders of magnitude greater throughput for fifth generation (5G) cellular systems. However, since mmWave signals are very susceptible to blockage, channel quality on any one mmWave link can be extremely intermittent. This paper implements a novel dual connectivity protocol that enables mobile user equipment (UE) devices to maintain physical layer connections to 4G and 5G cells simultaneously. A novel uplink control signaling system combined with a local coordinator enables rapid path switching in the event of failures on any one link. Based on this approach, this paper provides the first comprehensive evaluation of handover mechanisms in mmWave cellular systems. The simulation framework includes detailed measurement-based channel models to realistically capture spatial dynamics of blocking events, as well as the full details of MAC, RLC and end-to-end transport protocols. The study reveals significant benefits of the proposed method under several metrics, compared to conventional handover mechanisms.