Influenza virus neuraminidase (NA) is a major antiviral drug target and has recently reemerged as a key target of antibody-mediated protective immunity. Here we show that recombinant NAs across all non-bat subtypes adopt various tetrameric conformations, including a previously unreported 'open' state that may help explain poorly understood variations in NA stability across viral strains and subtypes. We used homology-directed protein design to uncover the structural principles underlying these distinct tetrameric conformations and stabilize multiple recombinant NAs in the 'closed' state. In addition to improving thermal stability, conformational stabilization improved affinity to protective antibodies elicited by viral infection, including antibodies targeting a quaternary epitope and the broadly conserved catalytic site. The stabilized NA proteins can also be integrated into viruses without affecting fitness. Our findings provide a deeper understanding of NA structure, stability, and antigenicity, as well as a roadmap towards structure-based discovery of NA-directed therapeutics and vaccines.