Deep learning researchers and practitioners usually leverage GPUs to help train their deep neural networks (DNNs) faster. However, choosing which GPU to use is challenging both because (i) there are many options, and (ii) users grapple with competing concerns: maximizing compute performance while minimizing costs. In this work, we present a new practical technique to help users make informed and cost-efficient GPU selections: make performance predictions using the help of a GPU that the user already has. Our technique exploits the observation that, because DNN training consists of repetitive compute steps, predicting the execution time of a single iteration is usually enough to characterize the performance of an entire training process. We make predictions by scaling the execution time of each operation in a training iteration from one GPU to another using either (i) wave scaling, a technique based on a GPU's execution model, or (ii) pre-trained multilayer perceptrons. We implement our technique into a Python library called Surfer and find that it makes accurate iteration execution time predictions on ResNet-50, Inception v3, the Transformer, GNMT, and DCGAN across six different GPU architectures. Surfer currently supports PyTorch, is easy to use, and requires only a few lines of code.