A new family Superornatiremidae is described from 7 inland marine caves of Bermuda and from Jameos del Agua Cave, a sea water-flooded Holocene lava tube on Lanzarote in the Canary Islands. The family is proposed to accommodate three new genera, Superornatiremis, Neoechinophora and Intercrusia, and six new species: S. mysticus, N. fosshageni, N. daltonae, N. jaumei, N. karaytugi and I. problematica. The major diagnostic character is the unique leg 1 which exhibits supernumerary elements on the proximal and middle exopod segments and the middle and distal endopod segments. The increase of armature elements is regarded as a secondary phenomenon in copepod evolution and not as the result of character reversal. Other unique characters comprise the presence of an epicopulatory flap closing off the copulatory pore, the laterally displaced female gonopores and the paired copulatory ducts, the modified trilobate proximal endite of the maxilla, the fused labrum and labium (derived from the fused paragnaths) forming a well developed oral cone, the modified endopod of leg 2 and the transformation of the distal inner seta of P2-P3 enp-3 into a spine. The family is further characterized by the complete lack of sexual dimorphism on the swimming legs. The three genera can be differentiated primarily by the combination of P1 armature, structure of the outer exopod spines of P1, genital field morphology and segmentation of the male PS. The problematic status of Intercrusia is discussed. The new family is placed in the tisbidimorph complex of families and seems to occupy an intermediate position between the two free-living tisbid subfamilies Tisbinae and Idyanthinae. The biogeography of the family is briefly discussed.