Opportunistic networks are characterised by intermittent connectivity, unstable topology, and no assurance of a fixed end-to-end path to transfer the messages because of nodes mobility. Due to this, the store-carry and forward mechanism is used for routing the data in such networks. Considering that the energy of relaying nodes during the routing operation get depleted, there is a clear demand for power-aware routing schemes for opportunistic networks. This article proposes an energyefficient altruism-based trust-dependent message forwarding routing protocol for opportunistic networks (called E-ATDTN), where social matrices are exploited to determine the trustworthiness of a node in participating in the message forwarding procedure. Extensive simulations are conducted to assess the performance of the newly proposed E-ATDTN protocol against that of the power-aware PRoPHET, energy efficient PRoWait, and power-aware EDR protocols showing that E-ATDTN outperforms E-PRoPHET, E-ProWait, and E-EDR in terms of average residual energy, overhead ratio, dropped messages, and number of dead nodes under varying time-to-live, and message generation interval.