Disk-shaped oceanographic buoys are commonly deployed with instrumentation to monitor and store localized environmental conditions for later transmission to passing oceanographic vessels or orbiting satellites for analysis and interpretation. The instrumentation and beacons are powered by battery packs and may utilize solar panels for recharging. Unfortunately, both the solar panels and instrumentation are too often vandalized. This research study investigates a SEAREV buoy design concept that features a pendulum wave energy conversion system inside an enclosure beneath the standard buoy hull. In this research study, a Lagrange formulation is used to develop equations of motion that are coupled with a hydraulic power take-off system. An in-house simulation model was selected to predict the buoy surge and pitch motions needed to estimate the electrical energy generated from a design seas. An iterative computational scheme was developed that utilizes an equivalent damping model of the power take-off system. The illustrative examples consider two four-meter disk buoys modified with a SEAREV wave energy conversion device, and they are subjected to relatively benign sea conditions using field measurements obtained by the National Oceanic and Atmospheric Administration (NOAA) in the Gulf of Mexico. A scatter diagram of the data was developed and used as the basis to estimate the buoy surge and pitch response and the resulting power generated. Bounded power estimates are presented and based on a limited survey of disk buoy power requirements; the predicted results for the system without optimization can provide four to five watts of power, and the findings are quite promising.