In order to visit archaeological sites, old forts etc., it is necessary to obtain a permit from the Ministry of Culture and National Heritage in Muscat. They are easy to obtain from the Ministry which is in the same building as the Natural History Museum in the Ministries Area of Medinat Qaboos. In some cases, the permit needs to be signed by the provincial governor. To be on the safe side, ask directions to the governor's office and get his signature.
In order to cross borders by land, a road permit is necessary. A road permit can be obtained in a few days through your sponsor. There is, however, a problem: the permits are not issued to single women. This is the only such travel restriction on single and/or unaccompanied women in the Sultanate.