Is there a particular naming convention for Java methods that throw exceptions?

Don't do that.

This is like asking "is there a naming convention for methods that take two Strings as parameters".

Java has checked exceptions, which means that you need to declare them anyway. So you can easily see if an exception will be thrown, and what type of exception. You cannot even compile code that calls the method without adding exception handling code.

Update: It seems your intention is to have methods that check if a certain condition is true, but you do not want to return just false, but throw an Exception if the condition is not met, so that you can also convey an explanation message (in the Exception). I think a prefix of "assert" or "ensure" makes sense:

 // instead of
 if (! isAuthenticated())
    throw new NotAuthenticatedException("not sure why at this point...");

 // you do
 assertAuthentication();
 // which will throw NotAuthenticatedException("proper explanation") inside

Why would you do such a thing in Java? It already has exception specifiers built into the language. The compiler will prevent you from calling a method which explicitly throws an exception without some action being taken on your part to handle or allow the exception to propagate?

Yes, you name them the same as methods that don't.

Isn't the exception specification enough?

Edit: If you have similar methods that throw/not throw, I recommend the Parse/TryParse pattern (Parse being replaced by the operation). .NET Framework uses it frequently (Dictionary<T,K>.TryGetValue, Monitor.TryEnter, int.TryParse, etc. etc.).

Edit: Coding Horror: TryParse and the Exception Tax

If you need these methods differentiated, I'm sure you can do it in the naming without using a suffix or anything, which is (as others have pointed out) pretty ghastly.

Why have:

boolean authenticate(String username, String password);

and (say)

void authenticateEx(String username, String password) throws WhateverException;

when you could actually make it a meaningful part of the name by conveying the actual intent:

void ensureCanAuthenticate(String username, String password);

// or

void assertValidCredentials(...);

// or

void authenticateOrDie(...);

... or any number of other (probably better) names which actually convey the intent rather than relying on a confusing suffix.