The development of ultrasmooth, macroscopic-sized silver (Ag) crystals exhibiting reduced losses is critical to fully characterize the ultimate performance of Ag as a plasmonic material, and to enable cascaded and integrated plasmonic devices. Here we demonstrate the growth of single-crystal Ag plates with millimetre lateral sizes for linear and nonlinear plasmonic applications. Using these Ag crystals, surface plasmon polariton propagation lengths beyond 100 μm in the red wavelength region are measured. These lengths exceed the predicted values using the widely cited Johnson and Christy data. Furthermore, they allow the fabrication of highly reproducible plasmonic nanostructures by focused ion beam milling. We have designed and fabricated double-resonant nanogroove arrays using these crystals for spatially uniform and spectrally tunable second-harmonic generation. In conventional 'hot-spot'-based nonlinear processes such as surface-enhanced Raman scattering and second-harmonic generation, strong enhancement can only occur in random, localized regions. In contrast, our approach enables uniform nonlinear signal generation over a large area.