Electrical connector that includes a connector housing having mating and terminating ends. The connector housing has a housing cavity and a leading edge at the mating end that defines an opening to the housing cavity. A central axis extends through the housing cavity between the mating and terminating ends. The electrical connector also includes a dielectric insert within the housing cavity and an electrical contact that is held by the insert along the central axis. The insert has a recess surface that faces the mating end and extends a radial distance, outward from the electrical contact. The insert includes a dielectric rim that projects from the recess surface toward the mating end. The dielectric rim surrounds: and is radially spaced from at least a portion of the electrical contact. The dielectric rim and the recess surface define an impedance-control space that surrounds at least the portion of the electrical contact.