Face　Super-Resolution　(FSR)　plays　a　crucial　role　in　enhancing　low-resolution　face　images,　which　is　essential　for　various　face-related　tasks.　However,　FSR　may　alter　individuals＇　identities　or　introduce　artifacts　that　affect　recognizability.　This　problem　has　not　been　well　assessed　by　existing　Image　Quality　Assessment　(IQA)　methods.　In　this　paper,　we　present　both　subjective　and　objective　evaluations　for　FSR-IQA,　resulting　in　a　benchmark　dataset　and　a　reduced　reference　quality　metrics,　respectively.　First,　we　incorporate　a　novel　criterion　of　identity　preservation　and　recognizability　to　develop　our　Face　Super-resolution　Quality　Dataset　(FSQD).　Second,　we　analyze　the　correlation　between　identity　preservation　and　recognizability,　and　investigate　effective　feature　extractions　for　both　of　them.　Third,　we　propose　a　training-free　IQA　framework　called　Face　Identity　and　Recognizability　Evaluation　of　Super-resolution　(FIRES).　Experimental　results　using　FSQD　demonstrate　that　FIRES　achieves　competitive　performance.