On Your Mark

They are both from the very famous studio Ghibli (Hayao Miyazaki, anyone?). Both are short music videos with similar art styles. 

Two emotional short animes somewhat revolves around the theme of freedom and happiness. 

Both are amongst the top 3 most popular professional standalone AMVs (which is a rare kind since most AMVs are either part of a series or fan-made assemblies of arbitrary anime scenes and music), the remaining one is Interstella5555, the longest music album video ever. The videos both have a sci-fi setting, On Your Mark has a retro touch whereas Shelter is more futuristic, however the songs and stories are fundamentally different. Also worth mentioning is that On Your Mark's screenplay was directed by no less than Hayao Miyazaki. 

Both are animated videos by Studio Ghibli (Producer of: Spirited Away, Princess Mononoke, My Neighbor Totoro, etc). Iblard Jikan: A moving paint with sound and music hung at your house showing you a beautiful world from another dimension - give a calm feeling. On your Mark: A short animated story between 2 policemen and a winged angel. Theme Song is "On Your Mark", a song by the Japanese rock duo Chage & Aska. 

Anime music videos with the premise of saving an angel 

Tsumiki no Ie and On your Mark are two non-speaking anime that succeed to bring a emotional story to the viewer even if they are both very short.