The title compounds, 2-(4-{2-[(2-oxo-2H-chromen-4-yl)oxy]acetyl}piperazin-1-yl)acetamide, C17H19N3O5, (I), and N-(2,4-dimethoxybenzyl)-2-[(2-oxo-2H-chromen-4-yl)oxy]acetamide, C20H19NO6, (II), are new coumarin derivatives. In compound (I), the six-membered piperazine adopts a chair conformation. The dihedral angles between the mean planes of the chromene ring and amide plane is 82.65 (7)° in (I) and 26.2 (4)° in (II). The dihedral angles between the mean planes of the chromene ring and the four planar C atoms of the piperazine ring in (I) and the benzene ring in (II) are 87.66 (6) and 65.0 (4)°, respectively. There are short intramolecular contacts in both molecules forming S(5) ring motifs, viz. N—H...N and C—H...O in (I), and N—H...O and C—H...N in (II). In the crystals of both compounds, molecules are linked by N—H...O hydrogen bonds, forming chains along [1\overline{1}0] in (I) and [010] in (II). The chains are linked by C—H...O hydrogen bonds, forming layers parallel to the ab plane in the crystals of both compounds. In the crystal of (I), there are also C—H...π and offset π–π interactions [intercentroid distance = 3.691 (1) Å] present within the layers. In the crystal of (II), there are only weak offset π–π interactions [intercentroid distance = 3.981 (6) Å] present within the layers. The intermolecular contacts in the crystals of both compounds have been analysed using Hirshfeld surface analysis and two-dimensional fingerprint plots.