Potentially useful experimental data takes many forms. The very nature of Monte Carlo simulation strongly supports the incorporation of any type of experimental constraint, because all you need it to do is allow it to influence the distribution of generated structures.
Rosetta calls constraints what other computational packages refer to as restraints. In Rosetta, a constraint does not fix a degree of freedom and remove it from sampling and scoring. Rather, we are adding a scoring term that penalizes deviations from particular values of that degree of freedom. Restraints have no particular name - it's just making sure that degree of freedom is not free, for example in a MoveMap.
Truly, the largest experimentally derived sampling bias to a biological problem is any input structures that might be available. After all, you are using those structures precisely because you trust them enough not to want to perform ab initio structure prediction, so you want the bias that starting from them provides. At the same time, input structures are not perfect:
Most of all, the force fields used in these optimization efforts are arithmetically and algorithmically distinct from the Rosetta energy function. It is critical to obtain structures that are geometrically similar to the starting structure but that exist closer to a local minimum of the scoring function. This is important because every unit of strain energy in your starting structure can inappropriately bias sampling: bad moves can be accepted that would otherwise have been rejected because they relieve strain that already should have been addressed. There is a complete write-up of preparing starting structures appropriately.
Rosetta has individual modules to handle particular forms of experimental constraint:
Frequently, you will encounter situations where you have knowledge about the experimental system that does not neatly fit into any of the above situations, or which provides very sparse or even conflicting information. This is all right: Rosetta's capacity for working with constraints: Guides to specific types of structural perturbations using RosettaScripts