A method of producing a land grid array (LGA) interposer structure includes mounting at least one interposer on a first surface of an electrically insulating carrier plane. The interposer selectively having a hemi-toroidal, conical, dome-shaped conic section, generally cylindrical or hemi-spherical configuration in transverse cross-section and being constituted of a dielectric elastomeric material. The method includes positioning a plurality of electrically-conductive elements about the surface of the hemi-toroidal interposer that extend radially inwardly and downwardly from an uppermost end thereof. The method further includes mounting said at least one component comprising at least one hemi-toroidal interposer mounted on said opposite side of said carrier plane. Additionally the method includes forming at least one through-extending via in said electrically-insulating carrier plane, and forming electrical connections between said first-mentioned at least one hemi-toroidal interposer and said further at least one inverted hemi-toroidal interposer.