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Unmanned Aerial Vehicle (UAV) technology is becoming increasingly used in a variety of applications such as video surveillance and deliveries. To enable safe and efficient use of UAVs, the devices will need to be connected into cellular networks. Existing research on UAV cellular connectivity shows that UAVs encounter significant issues with existing networks, such as strong interference and antenna misalignment. In this work, we perform a novel measurement campaign of the performance of a UAV user when it connects to an experimental two-tier cellular network in two different areas of Dublin city's Smart Docklands, which includes massive MIMO macrocells and wirelessly-backhauled small cells. We measure Reference Signal Received Power (RSRP), Reference Signal Received Quality (RSRQ), Signal to Interference and Noise Ratio (SINR), the downlink throughput, and the small cell handover rate. Our results show that increasing the UAV height reduces the performance in both tiers, due to issues such as antenna misalignment. The small cell tier, however, can maintain relatively stable performance across the entire range of UAV heights, suggesting that UAV users can successfully connect to small cells during their flight. Furthermore, we demonstrate that while the UAV handover rate significantly fluctuates at different heights, the overall observed handover rates are very low. Our results highlight the potential for small cells in urban areas to provide connectivity to UAVs.