The resilient operation of microgrids (MGs) relies strongly on their ability to operate in islanded mode, autonomously from the bulk grid, whilst adhering to secure operation requirements. Catastrophic events in the transmission grid can lead to abrupt MG islanding accommodated by large frequency and voltage excursions due to power imbalances within the MG. It is vital that MG scheduling algorithms incorporate both static and transient security metrics to ensure a secure transition during islanding, immunised against the transient phenomena. In this paper, we incorporate both frequency- and voltage-related security constraints in a MG operational planning problem to ensure robust operation against abrupt islanding events. We employ an iterative dynamic optimization approach, based on the sensitivities of active and reactive power injections to the system security metrics, to incorporate the transient and static security constraints in the planning problem. Due to their non-linear and intractable nature, the transient security constraints are reformulated as linear sequential resilience cuts resulting in a computationally efficient problem. The performance of the algorithm is shown on a 30-bus, 20 kV, distribution network, subject to a 24-hour variation in load and renewable generation.