The power grid is evolving into a smart grid due to the diverse energy generation and distribution. This complex grid has to be continuously monitored in real-time for its safe operation. Sensors known as phasor measurement units (PMUs) are used for obtaining health information pertaining to the grid in terms of time-synchronized voltage and current phasors. Measurements from several PMUs are sent through a synchrophasor communication network (SCN) to the phasor data concentrator (PDC). The PMUs, the PDC and the SCN together constitute the wide area measurement system (WAMS). Being an important constituent of the WAMS, the resiliency estimation of SCNs is paramount for their proper design. Resilience is a measure of the systems resistance to the disturbances or a measure of its ability to bounce back to a functional state in the event of failure. This paper presents a quantitative metric for estimating the resiliency of SCNs. Monte Carlo simulation (MCS) models are used to simulate random component failures, and the data is used for measuring the resiliency of the SCNs. A multi-objective genetic algorithm (GA) is used for optimizing the placement of PMUs and the PDC, to observe the power system with the minimum number of PMUs, and to simultaneously maximize the resilience. The practical power grid of West Bengal, India, is analyzed as a case study. This work can be a significant contribution to the power sector as it assists in the proper planning and placement of the communication infrastructure in a WAMS.