In some materials, the onset of superconductivity is accompanied by the spontaneous appearance of small magnetic fields. This is a signature of broken time-reversal-symmetry (TRS), and in several cases the origin is not understood. We aim to characterize the superconductivity of a new family of superconductors using muon-spin relaxation/rotation (MuSR), to both search for broken TRS and to determine the superconducting gap structure. MuSR is very sensitive to the internal fields in a sample and is therefore suitable for looking whether TRS is broken. In applied fields, the penetration depth and hence the superconducting gap symmetry can also be probed. Whether or not TRS is broken in this family will help us test recent theoretical proposals to explain this phenomenon. From combining these results with a theoretical analysis, the nature of the superconducting state can be determined.