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This paper presents a method for creating formally correct just-in-time (JIT) compilers. The tractability of our approach is demonstrated through, what we believe is the first, verification of a JIT compiler with respect to a realistic semantics of self-modifying x86 machine code. Our semantics includes a model of the instruction cache. Two versions of the verified JIT compiler are presented: one generates all of the machine code at once, the other one is incremental i.e. produces code on-demand. All proofs have been performed inside the HOL4 theorem prover.