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Cryptographic (crypto) API misuses often cause security vulnerabilities, so static and dynamic analyzers were recently proposed to detect such misuses. These analyzers differ in strengths and weaknesses, and they can miss bugs. Motivated by the inherent limitations of existing analyzers, we study runtime verification (RV) as an alternative for crypto API misuse detection. RV monitors program runs against formal specifications and was shown to be effective and efficient for amplifying the bug-finding ability of software tests. We focus on the popular JCA crypto API and write 22 RV specifications based on expert-validated rules in a static analyzer. We monitor these specifications while running tests in five benchmarks. Lastly, we compare the accuracy of our RV-based approach, RVSec, with those of three state-of-the-art crypto API misuses detectors: CogniCrypt, CryptoGuard, and CryLogger. RVSec has higher accuracy in four benchmarks and is on par with CryptoGuard in the fifth. Overall, RVSec achieves an average F1 measure of 95%, compared with 83%, 78%, and 86% for CogniCrypt, CryptoGuard, and CryLogger, respectively. We show that RV is effective for detecting crypto API misuses and highlight the strengths and limitations of these tools. We also discuss how static and dynamic analysis can complement each other for detecting crypto API misuses.