Low-frequency oscillations (LFO) are generated in interconnected electric networks because of the weak tie lines between the parts of the networks. Such oscillations have been a significant challenge for engineers that may lead to system instability if appropriate measures are not taken. This article proposes two new metaheuristic algorithms, the jellyfish search algorithm (JSA) and the tunicate swarm algorithm (TSA), to design the power system stabilizers (PSS) for single machine infinite bus (SMIB) and multimachine power system (MPS) networks. The proposed method uses the JSA and TSA to dampen out the LFOs by modifying the vital parameters of lead-lag type conventional PSS (CPSS). A damping ratio-based objective function improves both models' system damping. These methods are tested on an SMIB system and two distinct MPS networks exposed to the three-phase fault under various loading conditions. The effectiveness of the suggested approach has been studied by comparing the system eigenvalues and minimum damping ratio (MDR) produced from JSA and TSA-tuned PSS and the CPSS. In addition, time domain simulation results are compared, demonstrating that the new approach outperforms the standard techniques, such as particle swarm optimization (PSO) and backtracking search algorithm (BSA). In the SMIB system, MDR produced by JSA and TSA-based PSS is 2.55 times higher than that of CPSS. Similarly, in comparison to PSO and BSA-based PSS, JSA, and TSA-tuned PSS offer more than 1.4 times greater MDR in the Two Area Four Machine network and up to 8.4 times larger MDR for the IEEE-39 Bus network. Furthermore, the efficacy of the suggested JSA and TSA approaches' prediction capacity is validated by satisfying the values of statistical performance metrics.