A male coaxial connector structure for mating with a corresponding female connector structure to provide electrical connections at microwave frequencies, the female connector structure having a coaxial conductor structure with an outer conductor receptacle, the male coaxial connector structure comprising: a coaxial outer conductor structure having a central longitudinal axis and a central open region about the axis and having a face region at a leading end of the outer conductor structure, the outer conductor structure defining a continuous uninterrupted coaxial outer conductor surface; an outer compression finger structure disposed outside of and adjacent the coaxial outer conductor surface and having a plurality of longitudinally oriented slots having a length adequate to form individual finger regions comprising the compression finger structure and to ensure proper spring action of the finger regions; a center conductor pin structure disposed within the central open region and extending along the longitudinal axis; the face region of the coaxial outer conductor structure configured to contact a corresponding face surface of the coaxial outer conductor structure of the female conductor with the male and female connector structures mated together, providing intimate electrical contact between the coaxial outer conductors of the male and female connector structures, to provide an uninterrupted coaxial outer conductor system; characterized in that the finger regions of the outer compression finger structure are configured to compress to fit into the outer conductor receptacle of the female connector structure; and in that the finger regions of the outer compression finger structure terminate at a face recessed behind the face region of the coaxial outer conductive structure to ensure intimate contact between the face region and the corresponding face surface of the female conductor structure. a coaxial outer conductor structure having a central longitudinal axis and a central open region about the axis and having a face region at a leading end of the outer conductor structure, the outer conductor structure defining a continuous uninterrupted coaxial outer conductor surface; an outer compression finger structure disposed outside of and adjacent the coaxial outer conductor surface and having a plurality of longitudinally oriented slots having a length adequate to form individual finger regions comprising the compression finger structure and to ensure proper spring action of the finger regions; a center conductor pin structure disposed within the central open region and extending along the longitudinal axis; the face region of the coaxial outer conductor structure configured to contact a corresponding face surface of the coaxial outer conductor structure of the female conductor with the male and female connector structures mated together, providing intimate electrical contact between the coaxial outer conductors of the male and female connector structures, to provide an uninterrupted coaxial outer conductor system; characterized in that the finger regions of the outer compression finger structure are configured to compress to fit into the outer conductor receptacle of the female connector structure; and in that the finger regions of the outer compression finger structure terminate at a face recessed behind the face region of the coaxial outer conductive structure to ensure intimate contact between the face region and the corresponding face surface of the female conductor structure.