LED packages are provided that include a material that is both thermally conductive and has a coefficient of thermal expansion that is matched to that of an LED. The material can be a ceramic such as aluminum nitride. The package has a body that includes a bottom surface and a cavity disposed into the body. The cavity has a floor for bonding to the LED so that the LED sits within the cavity. The thermally conductive material is disposed between the floor of the cavity and the bottom surface of the package. The body can be fabricated from a number of layers where the thermally conductive material is in a layer disposed between the floor and the bottom surface. The other layers of the body can also be fabricated from the thermally conductive material. A light emitting device is made by attaching the LED to the LED package.