Many operators have been bullish on the role of millimeter-wave (mmWave) communications in fifth-generation (5G) mobile broadband because of its capability of delivering extreme data speeds and capacity. However, mmWave comes with challenges related to significantly high path loss and susceptibility to blockage. Particularly, when mmWave communication is applied to a mobile terminal device, communication can be frequently broken because of rampant hand blockage. Although a number of mobile phone companies have suggested configuring multiple sets of antenna modules at different locations on a mobile phone to circumvent this problem, identifying an optimal antenna module and a beam pair by simultaneously opening multiple sets of antenna modules causes the problem of excessive power consumption and device costs. In this study, a fast antenna and beam switching method termed Fast-ABS is proposed. In this method, only one antenna module is used for the reception to predict the best beam of other antenna modules. As such, unmasked antenna modules and their corresponding beam pairs can be rapidly selected for switching to avoid the problem of poor quality or disconnection of communications caused by hand blockage. Thorough analysis and extensive simulations, which include the derivation of relevant Cramér-Rao lower bounds, show that the performance of Fast-ABS is close to that of an oracle solution that can instantaneously identify the best beam of other antenna modules even in complex multipath scenarios. Furthermore, Fast-ABS is implemented on a software defined radio and integrated into a 5G New Radio physical layer. Over-the-air experiments reveal that Fast-ABS can achieve efficient and seamless connectivity despite hand blockage.