To be honest, about all I felt on my first solo dive was calm. I'd done all the preparation. I had an item-by-item checklist (in *very* fine detail) of every step I take gearing up. I had all my gear and knew it implicitly. I'd even talked to a couple intelligent and experienced divers.
With every buddy with whom I'd been diving, I'd felt like a poor substitute for a divemaster. I enjoyed diving with them, of course, but I felt I had to keep track of depths, ascent rates, NDLs, and even air for both of us, lest they overlook something and cause an incident. (Perhaps I was just being my overly-analytical self, or perhaps they were indeed a bit inexperienced and borderline dangerous without supervision.)
Anyway, when I did my first solo, it was like a breath of fresh air. I no longer had to watch anyone just in case they started swimming straight up after a cool looking fish. I didn't have to monitor anyone's air supply, NDLs, or anything. All I had to do was monitor myself and enjoy the dive. (Frankly, it really felt as if I had far fewer liabilities diving solo than with the buddies.) Since then, I've done quite a few solo dives. My significant buddy is currently in Japan where she teaches English classes, so I've had plenty of solo opportunity.
A later development, however, was my apparent positive influence on my significant buddy's older sister. She upgraded to AOW, took nitrox, and even concurred with my devious plan to have both of us in the same Rescue class (which did indeed turn out to be *much* more effective with two smart and dedicated divers). Anyway, I've had the privilege of making quite a few dives with her, now, and I must say that diving with an equally competent buddy is quite enjoyable, too.
I'm sure I'm going to do more solo. Diving recently with some other buddies, I again found myself thinking how much better it would be without having to alter my dive to suit their air consumption and low boredom threshold. (I can entertain myself watching a rock, even if I don't have a camera along.)
Anyway, I suppose what I'm rambling is that if you're the kind of person who tends to be dive shepherd, always watching everyone's depth and air and all, doing a first solo dive isn't really a "big deal". It takes more preparation and attention, of course, but at the same time, it can be quite calm (until you blow a LP hose and have to switch to your redundancy while at the bottom of the dive site... then it's exciting for a few moments).