ISO/IEC standardizes several chosen ciphertext-secure key encapsulation mechanism (KEM) schemes in ISO/IEC 18033-2. However, all ISO/IEC KEM schemes are not quantum resilient. In this paper, we introduce new isogeny-based KEM schemes (i.e., CSIDH-ECIES-KEM and CSIDH-PSEC-KEM) by modifying Diffie-Hellman-based KEM schemes in ISO/IEC standards. The main advantage of our schemes are compactness. The key size and the ciphertext overhead of our schemes are smaller than these of SIKE, which is submitted to NIST's post-quantum cryptosystems standardization, for current security analyses. Moreover, though SIKE is proved in the classical random oracle model, CSIDH-PSEC-KEM is proved in the quantum random oracle model. Finally, we discuss difficulty to construct isogeny-based KEM from ISO/IEC KEM schemes in the standard model (i.e., ACE-KEM and FACE-KEM).