(1) Background: Bees are the primary animal pollinators in most ecosystems, and honey bees (Apis mellifera L.) are important providers of pollination ecosystem services and products. Climate change is one of the major threats for honey bees. (2) Objectives and methods: Qualitative research using focus group discussions was carried out in northwestern Italy, to investigate the beekeepers’ perceptions of climate change effects, the relevant management adaptations, and the main issues affecting the sector. (3) Results: Beekeepers reported several consequences related to severe weather events (weakening or loss of colonies; scarcity of nectar, pollen, and honeydew; decrease or lack of honey and other bee products; greater infestation by varroa; decline in pollination), making it necessary to provide supplemental sugar feeding, intensive transhumance, more effective and sustainable techniques for varroa control, and increased production of nuclei. A strengths, weaknesses, opportunities, and threats (SWOT) analysis was completed, displaying the factors able to strengthen or weaken the resilience of the beekeeping sector to climate change. (4) Conclusions: Thanks to their strong motivation and collaborative attitude, beekeepers succeed in adopting farm and bee hive adaptation strategies that are able to limit the climatic adverse effects. However, these findings highlight how the institutional and financial support for the beekeeping sector should be strengthened and better targeted.