"No solution" is really the safest solution. Right now there is not a good mechanism for creating constants is Javascript, but if you establish a convention (ALL CAPS FOR CONSTS) to help identify them and do not overwrite them yourself then your own constants will be safe.
If you are writing a public library and you are really worried about someone modifying a value then you can use a private variable or return your constant from a function.
Use a function so the value cannot be modified:
var MY_CONSTANT = function() { return 42; }
alert(MY_CONSTANT()); // alerts "42"
Use a private value only accessible to your own code by using a closure:
(function() {
var MY_CONSTANT = 42;
alert(MY_CONSTANT()); // alerts "42"
...do other stuff in here...
})();
alert(MY_CONSTANT()); // alerts "undefined" because MY_CONSTANT is out of scope here