Backtesting risk measures is important for financial regulators to evaluate risk forecasts reported by financial institutions. As a natural extension to standard/traditional backtests, comparative backtests are introduced to compare different forecasting methods. Based on recently developed concepts of e-values and e-processes, we design a model-free method for standard backtests of identifiable risk measures. In addition, we develop model-free comparative backtests for elicitable risk measures by constructing e-processes. Our method can be applied to common risk measures including mean, variance, Value-at-Risk, Expected Shortfall, and expectiles. Simulation and real data analysis will be demonstrated as an illustration.