Methods for creating endofullerenes have been steadily improving since their discovery allowing for new types of endofullerenes to be created in larger numbers. When a molecule is trapped in a fullerene, the fullerene creates a harmonic trapping potential leaving most of the fundamental properties of the internal molecule intact. The fullerene cage does create a preferred axis for the internal molecule similar to studies of the alignment of molecules in the presence of an external electric field. We explore the alignment of AlF and N2 inside of C60. The interaction between the internal molecule and the fullerene cage is calculated using ab initio electronic structure methods. This interaction is then used to calculate the spectroscopic properties of the internal molecule. The internal molecules are found to be strongly aligned despite all spectroscopic constants calculated being relatively unaffected by the fullerene cage.