...The fundamental aspect of Rosh Hashanah is the idea of God's kingship. It is a day of coronation, and we are called upon to take our role in this coronation. The main theme is Kabbalat Ol Malchut Shamayim – accepting the kingship of Heaven, as heroically demonstrated by Avraham, who was prepared to follow the divine command [of the akeida] even though it contradicted his every emotion, every sensibility...From an essay by Rabbi Ari Kahn www.aish.com/tp/i/moha/48950996.html
God regarded Avraham's willingness to obey as equal to actual performance of the deed; He regarded the willingness to comply as fulfillment of the letter of His command.
...When Rosh Hashana falls on Shabbat and the Shofar is not sounded, we experience another intriguing repercussion of the akeida and of the sacrifice that was not made. The slaughter of Yitzchak was voided, yet God considered it as having been performed in full. Similarly, when we do not blow the Shofar, we are essentially performing an identical gesture and hoping that God accepts our lack of performance of the Mitzvah in a similar vein. This, too, is Kabbalat Ol Malchut Shamayim; in fact, it is an even more profound acceptance of God's rule. For when we blow the Shofar, we hear and accept God's Word, but when we desist from blowing the Shofar on Shabbat, we show concern for God's Shabbat, and we are effectively accepting not only the words of the Torah, but the words of the sages as well.
...Therefore, it is even more important when we don't blow the Shofar to concentrate and focus on how we accept God as King, how we adore and safeguard Shabbat, how we unswervingly accept the words of the Torah and the authority of the Rabbis. By not blowing the Shofar, we can bring about even greater Kabbalat Ol Malchut Shamayim.
Not Blowing Shofar: Kabbalat Ol Malchut Shamayim?
Interesting thoughts on not blowing shofar on Shabbat: