Just taking what would normally be a unit test and having the input values be generated. Some examples:
1. I have a test for encryption/decryption functions. The data that's provided for the plaintext, additional data, and key, is generated. The assertions are:
assert_ne!(plaintext, encrypted_data);
assert_eq!(plaintext, decrypted_data);
assert_eq!(aad, decrypted_aad);
etc
2. I have some generated integration tests. For example, in our product, there are certain properties that should always hold for a given database entry. I generate a new entry on every test and have the fields for that entry provided by quickcheck, then I perform the operation, query the database, and assert that properties on those values hold.
So to answer your question, yes. Sometimes you want to check a concrete output (ie: "this base64 encoded string should always equal this other value) for sanity, but in general property tests give me more confidence.
I find it works particularly well with a 'given, when, then' approach, personally.
edit: I'll also note that for the base64 case I'd suggest:
a) A hardcoded suite of values.
b) Generate property tests.
assert_eq!(value, base64decode(base64encode(value));
As well as things like "contains only these characters" and "ends with [=a-zA-Z]" etc.
c) Oracle tests against a "known good" implementation.