Resilient mounting clips, panel mount systems including the same, and associated methods. A resilient mounting clip includes a support structure engagement portion and a panel engagement portion with a plurality of edge extensions and a plurality of outboard panel supports. Each outboard panel support extends from a respective edge extension. Each outboard panel support is configured to move at least substantially parallel to a compression axis when the respective edge extension resiliently flexes with respect to the support structure engagement portion. A panel mount system includes at least one support structure, at least one resilient mounting clip, and at least two panels received by each mounting clip. A method of assembling a panel mount system includes positioning and securing a resilient mounting clip on a support structure and receiving each of a first panel and a second panel with the resilient mounting clip.