Load-flow analyses of islanded microgrids commonly assumes constant line admittances with respect to the grid's nominal frequency. This article analyzes errors resulting from this assumption and leverages the versatile modified-augmented-nodal analysis (MANA) formulation to propose new algorithms to account for the frequency in line admittances in load-flow calculations. The tests are implemented on an isolated 25-bus microgrid and an isolated 906-bus grid. Simulations for different loading scenarios illustrate the benefits of our approaches to the solution accuracy, especially for loadability assessment. In moderate loadability settings, the new block-dishonest Newton-Raphson method is shown to be the most efficient of the proposed algorithms. When close to the maximum loadability point, the frequency-dependent method has better performance.