Disclosed herein are compositions comprising an NSAID such as meloxicam and/or rizatriptan in combination with a cyclodextrin and/or a bicarbonate. These compositions may be orally administered, for example, to improve the bioavailability or pharmacokinetics of meloxicam and/or rizatriptan for the treatment of pain such as migraine, arthritis, and other conditions. Also disclosed herein are methods of treating pain, such as migraine, comprising administering meloxicam and rizatriptan to a human being suffering from pain, such as migraine. For migraine, these methods may be particularly useful when the meloxicam and rizatriptan are administered while the human being is suffering from an acute attack of migraine pain or migraine aura.