There are many important applications for real-time, autonomous classification of satellite images in the field of remote sensing (RS). Convolutional neural networks (CNN) have been shown to yield the highest classification accuracies in this field. However, typical CNN-based methods require large amounts of labeled training data to perform well, which is time-consuming and laborious to obtain. Few-shot learning is explored as a practical solution to enable fast adaptation to novel classes with few labeled samples. Two few-shot algorithms, namely Prototypical Networks and LaplacianShot, were explored in this work. However, the performance of these methods depends on pre-training on an abundance of related data, which may not necessarily be available in RS. To address this requirement, this research contributes insights into a more realistic satellite image classification scenario where novel class samples are scarce and have different spatial resolutions than existing labeled data. In this work, the aforementioned few-shot learning methods were compared to traditional supervised learning methods, specifically SVM and CNN fine-tuning. Ablation experiments were conducted to examine performance across varying amounts of training samples and the effect of pre-training the backbone on different publicly available RS datasets. Results show that few-shot methods fine-tuned on domain-relevant data demonstrate improved accuracies by up to 18% for novel tasks in a 5-way 1-shot scenario compared to using an out-of-domain backbone. In addition, LaplacianShot outperforms traditional training methods by 4.0% in 5-way 1-shot tasks even without fine-tuning on domain-specific data, demonstrating viability for few-shot algorithms in extremely data-constrained situations.