How do I keep aspect ratio on scalable, scrollable content in WPF?

You need to put the content (the grid) inside a Viewbox and set the Viewbox.Stretch Property to Stretch.Uniform

The Viewbox control is used to stretch or scale a child element and lets you control the way the child is stretched. Check the examples here.

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In this instance, your best bet is a UniformGrid. This is only useful if you want NxN grids.