Renewable energy sources are likely to become essential due to continuously increasing energy demands together with the depletion of natural resources that are currently used for power generation, such as coal and gas. They are also advantageous in terms of their reduced environmental impact. Here, the generation of electrical power from Vortex-Induced Vibration (VIV) of a cylinder is investigated numerically. The cylinder is free to oscillate in the direction transverse to the incoming flow. The cylinder is attached to a magnet that can move along the axis of a coil made from conducting wire. The magnet and the coil together constitute a basic electrical generator. When the cylinder undergoes VIV, the motion of the magnet creates a voltage across the coil, which is connected to a resistive load. By Lenz's law, induced current in the coil applies a retarding force to the magnet. Effectively, the electrical generator applies a damping force on the cylinder with a spatially varying damping coefficient. For the initial investigation reported here, the Reynolds number is restricted to Re <= 200, so that the flow is laminar and two-dimensional (2D). The incompressible 2D Navier-Stokes equations are solved using an extensively validated spectral-element based solver. The effects of the electromagnetic (EM) damping constant xi(m), coil dimensions (radius a, length L), and mass ratio on the electrical power extracted are quantified. It is found that there is an optimal value of xi(m) (xi(opt)) at which maximum electrical power is generated. As the radius or length of the coil is increased, the value of xi(opt) is observed to increase. Although the maximum average power remains the same, a larger coil radius or length results in a more robust system in the sense that a relatively large amount of power can be extracted when xi(m) is far from xi(opt) unlike the constant damping ratio case. The average power output is also a function of Reynolds number, primarily through the increased maximum oscillation amplitude that occurs with increased Reynolds number at least within the laminar range, although the general qualitative findings seem likely to carry across to high Reynolds number VIV.