Interlocking modular connectors or headers Have flexible tongue and groove structures for forming a variety of header assembly configurations. The interlocking modular headers can have locking structures in addition to the tongue and groove mating structures for permanently interlocking the modular headers together. The locking structures can include opposing ramps having locking surfaces that engage each other and prevent sliding disengagement of the modular headers in one direction and the grooves can include stop members to prevent sliding disengagement in the opposite direction. The tongues and grooves can have a dovetail shaped cross-section to allow some freedom of lateral movement between the interlocking modular headers in order for ramps to slide over each other and cause locking surfaces to engage and also to provide some independent flexibility to facilitate placement onto a mounting component and to withstand elevated temperatures.