A method is presented for synthesizing output estimators for a class of continuous time, uncertain, linear parameter-varying (LPV) systems. The uncertain system is described as an interconnection of a nominal LPV system and a block structured perturbation. The nominal LPV system is gridded over the space of parameters, with the state matrices being arbitrary functions of the parameters. The input/output behavior of the perturbation is described by integral quadratic constraints. The main contribution of this paper is the derivation of convex conditions for the synthesis of output estimators for uncertain, grid-based LPV plants. Since LPV systems do not have valid frequency response interpretations, the time domain, dissipation inequality approach is followed. Robust performance is measured using the upper-bound on the worst-case induced-L2 gain of the closed loop. The effectiveness of the proposed method is demonstrated using a numerical example.