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Continuum models to handle solvent and electrolyte effects in an effective way have a long tradition in quantum-chemistry simulations and are nowadays also being introduced in computational condensed-matter and materials simulations. A key ingredient of continuum models is the choice of the solute cavity, i.e. the definition of the sharp or smooth boundary between the regions of space occupied by the quantum-mechanical (QM) system and the continuum embedding environment. Although most of the solute-based approaches developed lead to models with comparable and high accuracy when applied to small organic molecules, they can introduce significant artifacts when complex systems are considered. As an example, condensed-matter simulations often deal with supports that present open structures. Similarly, unphysical pockets of continuum solvent may appear in systems featuring multiple molecular components. Here, we introduce a solvent-aware approach to eliminate the unphysical effects where regions of space smaller than the size of a single solvent molecule could still be filled with a continuum environment. We do this by defining a smoothly varying solute cavity that overcomes several of the limitations of straightforward solute-based definitions. This new approach applies to any smooth local definition of the continuum interface, being it based on the electronic density or the atomic positions of the QM system. It produces boundaries that are continuously differentiable with respect to the QM degrees of freedom, leading to accurate forces and/or Kohn-Sham potentials. Benchmarks on semiconductor substrates and on explicit water substrates confirm the flexibility and the accuracy of the approach and provide a general set of parameters for condensed-matter systems featuring open structures and/or explicit liquid components.