Contactless fingerprint recognition is an emerging biometric technology that has several advantages over contact-based schemes, such as improved user acceptance and fewer hygienic concerns. Like for most other biometrics, Presentation Attack Detection (PAD) is crucial to preserving the trustworthiness of contactless fingerprint recognition methods. For many contactless biometric characteristics, Convolutional Neural Networks (CNNs) represent the state-of-the-art of PAD algorithms. For CNNs, the ability to accurately classify samples that are not included in the training is of particular interest, since these generalization capabilities indicate robustness in real-world scenarios. In this work, we focus on the generalizability and explainability aspects of CNN-based contactless fingerprint PAD methods. Based on previously obtained findings, we selected four CNN-based methods for contactless fingerprint PAD: two PAD methods designed for other biometric characteristics, an algorithm for contact-based fingerprint PAD and a general-purpose ResNet18. For our evaluation, we use four databases and partition them using Leave-One-Out (LOO) protocols. Furthermore, the generalization capability to a newly captured database is tested. Moreover, we explore t-SNE plots as a means of explainability to interpret our results in more detail. The low D-EERs obtained from the LOO experiments (below 0.1% D-EER for every LOO group) indicate that the selected algorithms are well-suited for the particular application. However, with an D-EER of 4.14%, the generalization experiment still has room for improvement.