The His274→Tyr (H274Y) oseltamivir (Tamiflu) resistance mutation causes a substantial decrease in the total levels of surface-expressed neuraminidase protein and activity in early isolates of human seasonal H1N1 influenza, and in the swine-origin pandemic H1N1. In seasonal H1N1, H274Y only became widespread after the occurrence of secondary mutations that counteracted this decrease. H274Y is currently rare in pandemic H1N1, and it remains unclear whether secondary mutations exist that might similarly counteract the decreased neuraminidase surface expression associated with this resistance mutation in pandemic H1N1. Here we investigate the possibility of predicting such secondary mutations. We first test the ability of several computational approaches to retrospectively identify the secondary mutations that enhanced levels of surface-expressed neuraminidase protein and activity in seasonal H1N1 shortly before the emergence of oseltamivir resistance. We then use the most successful computational approach to predict a set of candidate secondary mutations to the pandemic H1N1 neuraminidase. We experimentally screen these mutations, and find that several of them do indeed partially counteract the decrease in neuraminidase surface expression caused by H274Y. Two of the secondary mutations together restore surface-expressed neuraminidase activity to wildtype levels, and also eliminate the very slight decrease in viral growth in tissue-culture caused by H274Y. Our work therefore demonstrates a combined computational-experimental approach for identifying mutations that enhance neuraminidase surface expression, and describes several specific mutations with the potential to be of relevance to the spread of oseltamivir resistance in pandemic H1N1.