In many European countries, the management of transport infrastructure networks faces major challenges due to such issues as climate change, ageing infrastructure facilities, new mobility technologies, and the energy transition. To deal with these challenges, public infrastructure administrators need to develop responsive and innovative solutions while at the same time sustaining and optimising current performance of the present infrastructure networks. This ability to balance innovation and optimisation is called ambidextrous capacity. In addition, developing and implementing new or improved solutions requires the capacity of an organisation to learn. This is especially challenging in project-oriented organisations, where innovations are explored in pilot projects, separated from production-oriented day-to-day processes. This paper aims to analyse what public infrastructure administrators can do to enhance ambidextrous and learning capacities to develop sustainable solutions and thereby enhance resilience. To this end, we studied the Dutch public infrastructure administrator Rijkswaterstaat. Based on the findings from our study, we propose three recommendations to public infrastructure administrators: (1) formulate and clearly communicate an overall strategy, and translate this strategy to the tactical and operational level, (2) use integrative tactics to overcome the drawbacks of the structural ambidexterity of projects, and (3) strengthen organisational learning by implementing supportive arrangements.