Methods of Electrical Discharge Machining (EDM) ceramic components are provided. In one aspect, a method includes electrical discharge machining a ceramic component, such as a Ceramic Matrix Composite (CMC) component. The ceramic component is electrical discharge machined while a contact matrix is positioned so that electrically conductive compliant and pressurized contacts of the contact matrix engage the ceramic component and so that an electrically conductive member of the contact matrix is in electrical conduction to a grounding structure.