Theoretical studies of the metamagnetism and anomalous phase of Sr(3)Ru(2)O(7) have focused on the role of van Hove singularities, although much experimental evidence points towards quantum criticality having a large effect. We investigate the magnetic and thermodynamic properties of systems where the magnetic field tunes through such a peak in the electronic density of states. We study the generic case of a van Hove singularity in 2D. We see that in combination with the requirements of number conservation and interaction effects the peak in the density of states produces several interesting phenomena including raising the critical field of the transition above naive estimates, altering the relationship between the temperature and field scales and creating a distinctive double-peak structure in the electronic specific heat. We show that this apparent non-Fermi liquid behaviour can be caused at mean-field level by a peak in the density of states.