An implant for sensing or/and measuring a physiological parameter in a subject's body organ separated by an organ wall, the implant comprising: an implant body comprising a rigid body wall (102, 125, 137) enclosing an inner lumen sized and configured for housing physiological parameter sensing or/and measuring means and an antenna configured for transmitting or/and receiving radio-frequency electromagnetic waves, said body wall (102, 125, 137) including coupling means at a proximal end thereof and configured for coupling with a distal end of an implant deployment device; and a septum gripper comprising a flexible gripping sleeve comprising an electrically conductive material encapsulated by an electrically non-conductive layer, said gripping sleeve being configured and selectively shapeable from a radially narrowed and axially stretched form, sized to pass through a septum opening in the organ wall, to a radially expanded form, suitable for gripping onto the organ wall from opposite sides thereof and around said septum opening, such that said implant body is fixatable or/and stabilizable across the organ wall and through said septum opening, so as to facilitate the sensing or/and measuring in the subject's body organ, wherein: (i) a distal end of the gripping sleeve is fixedly connected to a periphery of said rigid body wall (102, 125, 137) at a sleeve fixation area between a center point and a distal end of said body wall (102, 125, 137); (ii) a proximal end of the septum gripper comprises a sliding element made from a non-conductive material, configured to slide axially relative to the implant body, so that the gripping sleeve transitions selectively between the radially narrowed and axially stretched form and the radially expanded form; and (iii) said rigid body wall (102, 125, 137) includes an electrically non-conductive wall section housing the antenna. an implant body comprising a rigid body wall (102, 125, 137) enclosing an inner lumen sized and configured for housing physiological parameter sensing or/and measuring means and an antenna configured for transmitting or/and receiving radio-frequency electromagnetic waves, said body wall (102, 125, 137) including coupling means at a proximal end thereof and configured for coupling with a distal end of an implant deployment device; and a septum gripper comprising a flexible gripping sleeve comprising an electrically conductive material encapsulated by an electrically non-conductive layer, said gripping sleeve being configured and selectively shapeable from a radially narrowed and axially stretched form, sized to pass through a septum opening in the organ wall, to a radially expanded form, suitable for gripping onto the organ wall from opposite sides thereof and around said septum opening, such that said implant body is fixatable or/and stabilizable across the organ wall and through said septum opening, so as to facilitate the sensing or/and measuring in the subject's body organ, wherein: (i) a distal end of the gripping sleeve is fixedly connected to a periphery of said rigid body wall (102, 125, 137) at a sleeve fixation area between a center point and a distal end of said body wall (102, 125, 137); (ii) a proximal end of the septum gripper comprises a sliding element made from a non-conductive material, configured to slide axially relative to the implant body, so that the gripping sleeve transitions selectively between the radially narrowed and axially stretched form and the radially expanded form; and (iii) said rigid body wall (102, 125, 137) includes an electrically non-conductive wall section housing the antenna. (i) a distal end of the gripping sleeve is fixedly connected to a periphery of said rigid body wall (102, 125, 137) at a sleeve fixation area between a center point and a distal end of said body wall (102, 125, 137); (ii) a proximal end of the septum gripper comprises a sliding element made from a non-conductive material, configured to slide axially relative to the implant body, so that the gripping sleeve transitions selectively between the radially narrowed and axially stretched form and the radially expanded form; and (iii) said rigid body wall (102, 125, 137) includes an electrically non-conductive wall section housing the antenna.