The phrase "strong guarantees" means that something is promised to happen or be true, and there is a high level of confidence that it will actually happen or be true. Full definition
As a result of the national concern that was generated, indigenous people were given stronger guarantees in the new constitution. (goldmanprize.org)
Information about the security of a single function — which can often be determined through a fairly simple analysis — can provide strong guarantees about the security of an encryption scheme as a whole. (sciencedaily.com)
Did their agent convince them to pay a higher commission to get stronger guarantees? (glenndaily.com)