Mr Happy: There may be a standard method (but I think not).
So, what I have done in the past, and which seems to work. Remembering that you can't do a clicky until you know the thread ID, you must post the new thread first. This often leads to last minute entries in the old thread, putting it ahead of the new thread in the list.
So,
1,think of title for new thread
2,Check 'Thread ID of old thread' either write it down, or, if crafty, cut'n'paste from the current address (e.g. this one shows in current address as "http://www.mudcat.org/thread.cfm?threadid=19340#750935". you need only cut'n'paste the bit between the "org/" and the "#". i.e "thread.cfm?threadid=19340")
3, compose the initial message for the new thread, referring back to the old with a clicky. E.g see [a href=thread.cfm?threadid=19340]Name of Old Thread[/a] (in practise, the square brackets "[" should be the 'less than & greater than'"<" brackets., and the bit after the "a href=" is the cut'n' paste you made.
4,Submit this as your new thread.
5,Note the address of this new thread (as in 2 above)
6,Post message at end of old thread with a "clicky" to the new thread. (In this final message I always try and leave several blank lines before a final comment [say 6 line breaks] to the effect "Please post all messages to the new thread")
7,Check the list of current threads to ensure that the new one is higher up the list, if not, refresh it.

It is worth composing both messages in something like wordpro, on separate pages as 'old thread' & 'new thread', and minimising them on your tool bar. You can then post the 'new' message by starting a new thread, and pasting your message. Note the new thread ID, type it into your 'old thread' message, and cut'n'paste that. This reduces the time between posting the two messages, and avoids a rush job.

Nigel