Models for hydration effects that treat the solute and solvent as dielectric continua with different dielectric constants have achieved considerable popularity in recent years. Here we compare such models with microscopic molecular dynamics simulations for a variety of conformational transitions in peptides. The conformational changes studied include changing backbone torsion angles in the alanine dipeptide; formation of hydrogen bonds of the sort seen in antiparallel B-sheets in formamide and alanine dipeptide dimers; transitions from type I to type II beta-turns; and propagation of an alpha-helix from the N- and C-terminal ends. In each case, the peptide solute is described with the CHARMM-19 force field, and continuum solvent models (determined from finite-difference solutions to the Poisson equation and a surface-area term) are compared to free energy simulations using explicit TIP3P water as a solvent. In general, the agreement between the two theoretical methods is good, but "solvation" of a CHARMM-19 solute with TIP3P water tends to modify the gas-phase conformational energy differences to a greater extent than "solvation" with the continuum dielectric model. The need for consistency between the force-field charges and the continuum-model charges in calculations of this kind is demonstrated.