Inclining tests measure the edge of a ship's stability

Do navies use inclining tests to establish a warship's stability curve?

Yes. The ship is deliberately heeled, often alongside with cranes available to control the movement, so engineers can identify the stability limit.

The preferred setting keeps the ship near the pier and uses external control to stop the evolution before the vessel goes over. The loads can still be severe enough to carry cranes or nearby equipment with the ship when a test goes wrong, so a nominally static experiment still belongs in the risk-managed trial program.