Latency-insensitive design mitigates increasing interconnect delay and enables productive component reuse in complex digital systems. This design style has been adopted in high-level design flows because untimed functional blocks connected through latency-insensitive interfaces provide a natural communication abstraction. However, latency-insensitive design with high-level languages also introduces a unique set of verification challenges that jeopardize functional correctness. In particular, bugs due to invalid consumption of inputs and deadlocks can be difficult to detect and debug with dynamic simulation methods. To tackle these two classes of bugs, we propose formal model checking methods to guarantee that a high-level latency-insensitive design is unaffected by invalid input data and is free of deadlock. We develop a well-structured verification wrapper for each property to automatically construct the corresponding formal model for checking. Our experiments demonstrate that the formal checks are effective in realistic bug scenarios from high-level designs.