Kernel survival analysis methods predict subject-specific survival curves and\ntimes using information about which training subjects are most similar to a\ntest subject. These most similar training subjects could serve as forecast\nevidence. How similar any two subjects are is given by the kernel function. In\nthis paper, we present the first neural network framework that learns which\nkernel functions to use in kernel survival analysis. We also show how to use\nkernel functions to construct prediction intervals of survival time estimates\nthat are statistically valid for individuals similar to a test subject. These\nprediction intervals can use any kernel function, such as ones learned using\nour neural kernel learning framework or using random survival forests. Our\nexperiments show that our neural kernel survival estimators are competitive\nwith a variety of existing survival analysis methods, and that our prediction\nintervals can help compare different methods' uncertainties, even for\nestimators that do not use kernels. In particular, these prediction interval\nwidths can be used as a new performance metric for survival analysis methods.\n