If you need to call into user-generated Javascript synchronously or have greater control over the sandbox environment, you can use WebAssembly to run a Javascript interpreter: https://github.com/justjake/quickjs-emscripten#quickjs-emscr...
QuickJS in WebAssembly is much slower than your browser's native Javascript runtime, but possibly faster than async calls using postMessage. As an added bonus, it can make async functions in the host appear to be synchronous inside the sandbox using asyncify: https://github.com/justjake/quickjs-emscripten#async-on-host...