Any state that does not include California, Arizona, New Mexico and Texas.
The four Southwestern state of the US that are all on the border of Mexico are Texas, California, New Mexico and Arizona. From West to East they would be; California, Arizona, New Mexico and Texas.
Depending on how you define Southwestern states, you have Arizona and New Mexico for certain. California and Texas can be added to your list if your definition is broad enough. All of these states border Mexico. None of the states on the Canadian border would be considered "southwetern".
It shares a common border with the Southwestern states of Texas, New Mexico, Arizona and California.
Montana does not border Mexico.
Mexico borders the Southwestern states of Arizona, New Mexico and Texas.
Southeastern
Arizona lies in the southwestern United States, on the border with Mexico. The state is bordered by Utah to the north, by New Mexico to the east, to the south by the states of Sonora and Baja California (Mexico), and to the west by California and Nevada.
Arizona ("AZ") lies in the southwestern United States, on the border with Mexico.
The state of New Mexico is located in the southwestern United States, along the U.S.-Mexico border. Mexico (the country) on the other hand, is along the southern boundary of the United States, bordering California, Arizona, New Mexico and Texas.
The southwestern state that does not touch a foreign country is New Mexico. While it shares borders with several U.S. states, including Texas, Arizona, Utah, and Colorado, it does not have a border with any foreign country like its neighbors to the south and west. New Mexico is landlocked in terms of international borders, making it unique among southwestern states.
There are two of them; one is known as Sierra Madre del Sur and runs from southwestern Jalisco to the east of the state of Oaxaca; the other one is the Sierra de Chiapas which runs along that state weastward into the Mexico-Guatemala border.
If you mean NEW Mexico, it is a state located in the southwestern United States.