A seal system for a gas turbine engine that extends along an axial centerline, comprising: a support structure; a rotor; and a floating non-contact seal, the floating non-contact seal comprising: a support ring; at least one beam coupled to the support ring; and a shoe coupled to the at least one beam, the shoe having an axial shoe face, wherein an axial clearance is defined between the axial shoe face and a support structure face of the support structure when the seal is subjected to a pressure load below a first threshold, and the axial shoe face includes a rounded edge that is configured to contact the support structure face of the support structure when the seal system is subjected to a pressure load (350; 350'; 350") that is equal to or greater than the first threshold, the shoe having a radial shoe face opposed to a rotor face of the rotor; characterised in that: the shoe is configured to fully translate relative to the support structure in a radial direction when the pressure load (350; 350'; 350") is greater than the first threshold and less than a second threshold; and the shoe is configured to rotate about the contact between the rounded edge and the support structure face instead of translating when the pressure load (350; 350'; 350") is greater than the second threshold. a support structure; a rotor; and a floating non-contact seal, the floating non-contact seal comprising: a support ring; at least one beam coupled to the support ring; and a shoe coupled to the at least one beam, the shoe having an axial shoe face, wherein an axial clearance is defined between the axial shoe face and a support structure face of the support structure when the seal is subjected to a pressure load below a first threshold, and the axial shoe face includes a rounded edge that is configured to contact the support structure face of the support structure when the seal system is subjected to a pressure load (350; 350'; 350") that is equal to or greater than the first threshold, the shoe having a radial shoe face opposed to a rotor face of the rotor; a support ring; at least one beam coupled to the support ring; and a shoe coupled to the at least one beam, the shoe having an axial shoe face, wherein an axial clearance is defined between the axial shoe face and a support structure face of the support structure when the seal is subjected to a pressure load below a first threshold, and the axial shoe face includes a rounded edge that is configured to contact the support structure face of the support structure when the seal system is subjected to a pressure load (350; 350'; 350") that is equal to or greater than the first threshold, the shoe having a radial shoe face opposed to a rotor face of the rotor; characterised in that: the shoe is configured to fully translate relative to the support structure in a radial direction when the pressure load (350; 350'; 350") is greater than the first threshold and less than a second threshold; and the shoe is configured to rotate about the contact between the rounded edge and the support structure face instead of translating when the pressure load (350; 350'; 350") is greater than the second threshold. the shoe is configured to fully translate relative to the support structure in a radial direction when the pressure load (350; 350'; 350") is greater than the first threshold and less than a second threshold; and the shoe is configured to rotate about the contact between the rounded edge and the support structure face instead of translating when the pressure load (350; 350'; 350") is greater than the second threshold.