I should preface this by saying I wasn't entirely happy with the one fitting I had. But I made a point of finding a saddle that worked before I went for the fit. In fact, the saddle was a large part of the reason why I decided the fitting was necessary - it completely changed the way I sat on the bike.
I did know that the shop where I had my fit done didn't stock any saddle that had a hope of working for me. Maybe if you were getting fitted at a shop that had a wide selection of saddles in sizes and shapes that you think might possibly work for you, you should get it all done at once.
Speed comes from what you put behind you. - Judi Ketteler