Selection of the interruption capabilities of HVDC circuit breakers (DCCB) requires an estimation of the maximum DC-side fault current and absorbed energy. However, estimating these requires iterating over a large range of scenarios. At present, this task is performed for a specific grid using extensive time domain simulations in Electromagnetic Transient (EMT)-type software. These simulations require a large computational effort, especially for large-scale meshed HVDC grids. In this paper, an alternative DC-side fault current estimation approach based on numerical inverse Laplace transform is proposed to reduce the computational burden in estimating the DCCB parameters without the need for extensive EMT simulations. The proposed approach includes the pre-fault conditions, stages of the converter fault response, DCCB operation and detailed transmission line model. The paper shows that the fault current interruption and absorbed energy in the DCCB, can be approximated accurately for the DCCB operating times within the first two stages of the converter fault response, while an upper limit of these quantities can be estimated for DCCBs operating within the subsequent stages. The proposed approach allows for investigating a large range of scenarios in large-scale meshed HVDC grids with acceptable computational effort, sufficient accuracy and adaptability to system configuration/parameter changes.