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On Rosh Hashanah, the night Kiddush is similar to that of the other festivals. Where it differs, it is usually to follow the pattern of middle blessing of the Amidah. (An example is the concluding formula "Blessed are You, the LORD, King over the entire world, Who sanctifies Israel, and the Day of Remembrance.") During the day, the verses Psalms 81:4-5 are recited prior to the blessing over wine. Many also say the festival verses (usually first), and on Shabbat all recite the relevant verses (see above) at the very beginning.
On Yom Kippur, no kiddush is recited, even by one who will be eating, and even on Shabbat.
When a festival is on Saturday night, Kiddush is recited, but Havdalah must also be said because Shabbat is holier than the festivals. The sequence of blessings in such a case is known as yak'n'haz (יקבה"ז), for yayin, kiddush, ner, havdalah, zman, meaning "wine, kiddush, flame, havdalah, shehecheyanu". That is, first the blessing over wine, then the standard kiddush blessing (see above), then the blessing for the flame (borei m'orei ha'eish, Who creates the radiance of the fire), then a modified havdalah blessing (ending with "Who differentiates between (one level of) holiness and (another level of) holiness"), and then the shehecheyanu blessing (omitted on the final days of Passover; see above). Essentially, the hvadalah blessings are recited after kiddush, but before shehechiyanu, which is usually the last blessing to ever be recited. Spices are not used.
In the opposite case, when Shabbat follows a festival, the regular Shabbat kiddush is recited, with no variations.
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