Multi-Agent Meeting (MAM) is the problem of finding a meeting location for multiple agents and paths to that location. Practically, a solution to MAM may contain conflicting paths. A related problem that plans conflict-free paths to a given set of goal locations is the Multi-Agent Path Finding problem (MAPF). In this paper, we solve the Conflict-Free Multi-Agent Meeting problem (CF-MAM). In CF-MAM, we find a meeting location for multiple agents (as in MAM) as well as conflict-free paths (as in MAPF) to that location. We introduce two novel algorithms, which combine MAM and MAPF solvers, for optimally solving CF-MAM. We prove the optimality of both algorithms and compare them experimentally, showing the pros and cons of each algorithm.