Oseltamivir-resistant influenza viruses arise due to amino acid mutations in key residues of the viral neuraminidase (NA). These changes often come at a fitness cost; however, it is known that permissive mutations in the viral NA can overcome this cost. This result was observed in former seasonal A(H1N1) viruses in 2007 which expressed the H275Y substitution (N1 numbering) with no apparent fitness cost and lead to widespread oseltamivir resistance. Therefore, this study aims to predict permissive mutations that may similarly enable fit H275Y variants to arise in currently circulating A(H1N1)pdm09 viruses. The first approach in this study utilized in silico analyses to predict potentially permissive mutations. The second approach involved the generation of a virus library which encompassed all possible NA mutations while keeping H275Y fixed. Fit variants were then selected by serially passaging the virus library either through ferrets by transmission or passaging once in vitro. The fitness impact of selected substitutions was further evaluated experimentally. The computational approach predicted three candidate permissive NA mutations which, in combination with each other, restored the replicative fitness of an H275Y variant. The second approach identified a stringent bottleneck during transmission between ferrets; however, three further substitutions were identified which may improve transmissibility. A comparison of fit H275Y variants in vitro and in experimentally infected animals showed a statistically significant correlation in the variants that were positively selected. Overall, this study provides valuable tools and insights into potential permissive mutations that may facilitate the emergence of a fit H275Y A(H1N1)pdm09 variant. IMPORTANCE Oseltamivir (Tamiflu) is the most widely used antiviral for the treatment of influenza infections. Therefore, resistance to oseltamivir is a public health concern. This study is important as it explores the different evolutionary pathways available to current circulating influenza viruses that may lead to widespread oseltamivir resistance. Specifically, this study develops valuable experimental and computational tools to evaluate the fitness landscape of circulating A(H1N1)pmd09 influenza viruses bearing the H275Y mutation. The H275Y substitution is most commonly reported to confer oseltamivir resistance but also leads to loss of virus replication and transmission fitness, which limits its spread. However, it is known from previous influenza seasons that influenza viruses can evolve to overcome this loss of fitness. Therefore, this study aims to prospectively predict how contemporary A(H1N1)pmd09 influenza viruses may evolve to overcome the fitness cost of bearing the H275Y NA substitution, which could result in widespread oseltamivir resistance.