Reading the above two comments, I agree with so much that has been stated, and feel that each person's success at achieving a desired range will be a unique path traveled by each and every one posting, but with some commonly shared way stations along this path.
My common experience: "If you wanted to improve your mile time, you wouldn't wake up one morning and decided to gain a minute. It doesn't work that way. Why would instrument playing be any different?" So true. My travels to increasing range came over time with lot's and lot's of practice time, to where I found (for me) to advance and even more importantly, maintain, I HAVE to practice at least an hour a day, with an optimal daily goal of 1.5 hours. This is the only way to develop and maintain muscle (lips, chest, abdomen) to get there. Just working on the horn for that hour and a half, I met my first goal of having a full sounding (strong and hit solidly greater than 95% of the time) C above staff to the F above that one upon graduating college. I needed that full strength and certain F to meet the demands of lead parts I was given in Graduate School. With the above practice time and rehearsing the charts from the band judiciously, I achieved that solid F within 6 months. My "method book" were the charts I used.
I was happy with that range for many years (1970 - 2004) that followed and had no reason to add to it... so didn't.
Then I joined a demanding quintet in 2004. No real "lead playing", but the original charts written by several of the band members were DEMANDING. Not demanding in going higher than G (one note above my solid F) but hanging above staff to about the range of E for over half of the duration of many of the charts. Just working on those tunes, and within months of rehearsing the band, playing two 4 hour gigs a week (on nights I did not practice) developed lip muscle I never intended to achieve. It was not really a conscious work routine, just playing really cool tunes that were highly motivating to play got me to a whole new level.
Fast Forward After about another 6 months of playing with this quintet, the quintet leader was insisting I share the lead part with his jazz orchestra, a position I really no longer aspired to doing after I played lead in Graduate School. But I highly respected this leader and amazingly found that I had a solid A when some of his big band charts had that note written in. Suddenly, I was hitting that note strong and solid at the 95% level. And you know at that point I found out, I could never miss that G below the A anymore. So then I set my goal to double high C so I could octave up from standard charts. Why? Because I wanted to see if I could do it (not that I had to do it).
So I started using the Cat Anderson method, and lip slur exercises in the high range given to me by a friend. Within a year, the double high C was strong at 95%. ANY NOTE below that is now nothing. It is the same feeling I have when weight lifting. Getting to 210 lbs took 2 years, and now I lift 210 every day, and it hurts, but that 180 lbs is like nothing to lift, and it took me a year just to get to that 180 lbs. And oh yes, I lift weights for an hour and a half a day, working on chest and abs and YES during the time I was going for the double high C. I found having such exhalation muscle reserve from this weight lifting routine ALSO had some effect on providing a scaffolding that assisted in supporting the 95% double high C, I learned that with the lower airway support, I could relax the embouchure. Relaxing. That opened up everything.
So now, do I use that high range regularly? Yes but in a different way from lead playing. I use it with nearly every song, I play in a small group ensemble near the climax of the solo, but do this as a quick phrase run and WITH AS LOW VOLUME as I can, to make it sing, not scream. Having this range under my belt has given me confidence to open up an improvisational execution of phrasing that I can do on a whim at any moment I choose it will work well into a solo. It has given me a performance voice that makes my sound unique.
All these years of playing, an working. I achieved confidence, not range, which was NEVER my original goal.
This is why I have created the saying: "Practice makes perfect, but nobody's perfect, so why practice?"
The answer to that question is: One should NEVER settle on perfection, as once you THINK you have achieved perfection, you have shorted yourself at going beyond perfection!