Diaphragmatic breathing provides the proper breath support necessary to hit the highest pitches in the vocal range. Without proper breath support, any attempts to increase your range results in severe limitations. To breathe correctly, you must pull air into the lungs using the diaphragm, to expand your stomach area and sides. Place your hand on your waist and take a deep breath. If you don't feel your sides and stomach expanding, you are not breathing correctly. To learn how to breathe deeply, practice yawning; yawning expands your stomach and sides in the way necessary to take a full breath.
Vocal warm-ups are an essential part of preparing your voice to sing higher. You can't walk into a performance and sing at the highest register without first getting your voice ready. Warming up helps you expand your range, lubricates the vocal folds, and prepares you to sing without damaging your voice. A good warm-up should include short five-note ascending and descending major scales in the middle of your range, followed by singing up and down major scales to gradually warm your throat. Drinking tea with honey also helps to warm up the vocal folds. The honey helps to coat your voice and remove any phlegm.
Buzzing the lips on higher pitches provides a safe way to increase your pitch without wearing down your voice. Start on a C major scale; a soprano should start an octave above middle C. Sing the first five chromatic notes above C so the last note is E. Continue to add a half-step to each note until you reach the highest portion of your range. When done, work on your lower range as well. Expanding the lower range increases your high register, since it helps to expand the length of your vocal folds. Practice the same exercise, but start on middle C, descending instead of ascending.
This vocal extension exercise directly affects your ability to sing in the highest range of your voice. Start a fifth below the highest note you can sing comfortably. For this purpose, the highest note should be easy to sing and shouldn't strain your voice at all. For most sopranos, a fifth below the highest pitch is an E or an F on the top of the treble clef. On half-notes sing upward chromatically five pitches. Hold the top note for four beats, then descend to the starting pitch. Start a half-step higher and attempt to go higher still. Continue this exercise until you can't sing higher. Take a 15-minute break and complete this exercise again.