Developing real-time routing protocols under energy constraint is one of the key points for providing end-to-end delay guarantee in multi-hop wireless sensor networks. In this paper, we give, at first, an overview of the existing real-time routing protocols and point out some potential approaches to improve them. To enhance existing protocols, one way is to make routing decision based on multi-hop rather than 1-hop neighborhood information. We study the asymptotic performance of a generic routing metric as the quantity of information a priori increases and propose then a 2-hop neighborhood information based real-time routing protocol. As an example, the approach of mapping packet deadline to a velocity is adopted as in SPEED; however, our routing decision is made based on the 2-hop velocity. An energy efficient probabilistic drop is proposed to improve energy utilization efficiency. When packet deadline requirement is not stringent, a design is integrated to release nodes from heavy consumption. Energy balance over nodes is thus improved. Simulation results show that, compared with protocol SPEED that only utilizes 1-hop information, the proposed scheme leads to lower deadline miss ratio and higher energy efficiency.