My TNG fu is failing me

[karohemd]

brrm posted this Star Trek vs. Star Wars video which is a little giggle but what I can't figure out is which episode the scene is from in which Picard stalls whoever he's talking to, walks over and wipes his finger across the top of the plaque (starting at 3:56). Help me, f-list, you're my only hope. It looks like an outtake or something because I really can't remember. The other characters in the background seem a bit off, too.

ETA: akcipitrokulo is the queen among TNG-heads. Don't look at the comments if you want to guess yourself.