Removing the Tefillin before Musaf:
The custom is to remove the Tefillin prior to the silent prayer of Musaf. This applies even in those communities that recite Nakadishach in Musaf. [This applies even for one who is Davening in private. According to Kabala, there is a grave prohibition against Davening Musaf with Tefillin.]
What is one to do if he is still wearing Tefillin by Kedusha of Musaf?
One is to remove the Tefillin prior to the Chazan reaching Keser. If one is unable to do so, such as he suddenly realized that the Chazan reached Keser, he is to move his Shel Rosh to the side of his head and place his Tallis, or a cloth, under his Shel Yad, thus making an interval between it and his arm. Alternatively, if one does not want to answer Kedusha, he is to leave to another room. Some Poskim rule that if one is prior to Shacharis, or prior to completing the prayer of Shacharis, one need not be particular against reciting Keser with the Tefillin. Many are accustomed to simply cover their Tefillin [and remain wearing them] upon the recital of Keser if they are not Davening with this Minyan of Musaf.
 Michaber 423/4; Rama 25/13; Admur 25/41; Siddur Admur
On Rosh Chodesh one is required to remove the Tefillin prior to the silent prayer of Musaf. [Michaber ibid] This applies in those communities that recite the Kedusha of Keser in Musaf, in which case the Tefillin is to be removed before Musaf, after having said the Kedusha of Uva Letzion, being that it is improper to be wearing Tefillin while saying Keser. Furthermore, even those communities who do not say Kedushas Keser in Musaf [but rather say Nakdishach] are accustomed to remove the Tefillin prior to Musaf. [Admur ibid; Rama ibid]
 The reason: As it is improper to be crowned with Tefillin while saying “Keser Yitnu Lecha”. [Admur ibid; M”A 25/32; Beis Yosef] Alternatively, the recital of Musaf is in place of the Karban Musaf, and during the time of the Musaf offering it is considered a Yom Tov, and Yom Tov contains an Os which is exempt from Tefillin. [Levush 25/13; 423; M”B 423/4; Kaf Hachaim 423/26] There is also a Kabbalistic reason mentioned behind this custom. [Shaar Hakavanos p. 38; Kaf Hachaim 423/26]
 Admur ibid and Rama ibid that so is the the custom; See Background
 See Zekan Ahron 2/5; Piskeiy Teshuvos 25/28
 Rashal in Yam Shel Shlomo Beitza 1/51; Bach 26 in name of Iggur, in name of Zohar, based on Midrash Hanelam Shir Hashirim that one who Davens with Tefillin during Musaf of Rosh Chodesh and Chol Hamoed is liable for death.
 Ben Ish Chaiy Vayikra 17; Torah Leshma; Kaf Hachaim 25/99; Piskeiy Teshuvos 25/28
 Piskeiy Teshuvos ibid
 Shulchan Hatahor 25/13; Ashel Avraham Butchach 25
 The reason: As one is still prior to receiving the Kedusha of Musaf and Yom Tov, and hence his Tefillin do not contradict the Keser being heard. [ibid] Perhaps, based on this, people who are in middle of Shacharis are accustomed to cover the Tefillin upon the Chazan reaching Musaf, but do not remove it. However see Admur ibid that one is not to recite the words Keser while wearing Tefillin, irrelevent of the concept of the Kedusha of Yom Tov. Vetzaruch Iyun!
 Miaseif Lechol Hamachanos 25/136; See previous footnote!