Fourth-order many-body perturbation-theory calculations of the spectroscopic constants of CaH+ are presented as an attempt to help identify possible astronomical or laboratory observations. The results for the rotational and vibrational constants are, respectively, 4.61 and 1511 cm . Similar calculations are made on MgH+, where comparison with experimental values shows excellent agreement, indicating reliable results for CaH+. PACS number(s): 31.20.Di, 33.20.Bx, 95.85.Bh