This Rosh Hashana, we will be without the mitzva from the Torah that is so central to the experience of the day, the blowing of the shofar. Not only do we miss the opportunity to do a mitzva, but it also makes us somewhat apprehensive going into our judgment without the protection it provides. How are we supposed to feel about missing the shofar?
The Netivot Shalom (Rosh Hashana 6) says that the sound of the shofar does actually accompany us. The mishna (Rosh Hashana 29b) says that when Rosh Hashana falls on Shabbat, the shofar is blown in the mikdash (sanctuary) but not in the medina (in the country, in general). The Beit Avraham is cited as saying that medina refers to actions that we do with our body, whereas mikdash refers to our minds. Indeed, without blowing the shofar this Shabbat, the concept of the shofar accompanies our minds.
The gemara (ibid.) says that we do not blow shofar out of concern that someone will carry it outside. The Yerushalmi attributes the lack of shofar blowing to p’sukim. One of the references to shofar blowing in the Torah calls Rosh Hashana a "day of blasts" (Bamidbar 29:1) whereas the other one refers to a "remembrance of blasts" (Vayikra 23: 24). When Rosh Hashana falls on Shabbat, we fulfill the element of remembrance. It is strange, though, that the first and more central of the discussions of Rosh Hashana should refer to the exception to the rule, when the shofar is missing. The Netivot Shalom answers that the "fulfillment" of shofar on Shabbat is actually the higher level: the remembrance of shofar is in our minds without needing the physical blowing. Usually, he explains, the shofar inspires us in the manner of yirah (fear of Heaven). Shabbat adds the element of ahava (love), which joins together with yirah to create a harmonious whole.
It is interesting that the word used to connote the involvement in shofar without the action, "zichron," shares the root of the word for the positive commandment of our commemoration of Shabbat, "zachor" (Shemot 20:8; see Berachot 20b). What great positive actions do we do to commemorate Shabbat? We make a declaration that the day is Shabbat (which rabbinically we enhance with wine and a longer than Biblically necessary recitation) and that’s it. Perhaps this is the idea of Shabbat. Hashem rested from activities and imbued the world with a special concept - that a thought-out refraining from activity can bring as much or more to the world as creating heavens, earth, and all that reside in them. Rosh Hashana corresponds to the sixth day of creation, when everything was completed - except Shabbat. When Shabbat coincides with Rosh Hashana, we cannot ignore Shabbat, and we introduce the element of contemplation on lofty ideals and ceasing to act within the commemoration of Rosh Hashana.
May we be able to experience Rosh Hashana with the sanctity of Shabbat that entered the world as its creation was completed and thereby coronate Hashem in a most significant way.