Validating an input string against some enum fields
I would pass a TestEnum instead of a String to your method, forcing the exception handling to be outside the method. I don't see why you are using Strings at all actually (although I suspect that this is only a small part of your code, and that you have your reasons for needing this).

I would do some refactoring and use EnumSet, which could make your code something like this: (untested code, but I believe it should work)

public static void main(String[] args) {
    String enumName = "h3";
    EnumSet&lt;TestEnum&gt; except = EnumSet.of(TestEnum.h1, TestEnum.h2, TestEnum.h3);

    boolean valid;
    try {
       valid = !except.contains(TestEnum.valueOf(enumName));
    } catch (IllegalArgumentException e) { valid = false; }
    System.out.println(valid ? "valid" : "invalid");
}


Note that I have gotten rid of your entire method here as I think that when you use EnumSet like this, you don't need the method. But of course you can put the relevant parts of the above code into a method.