Physical Unclonable Functions (PUFs) are a very useful resource in cryptography with many applications ranging from system authentication to secret key generation. Side-channel attacks (SCAs) are a major concern in any physical implementation of a cryptographic module, and PUFs are no exception. Electromagnetic (EM) leakage from the implementation of a ring-oscillator-based PUF (RO-PUF) can be exploited to retrieve sensitive information that compromises the security of the cryptographic scheme incorporating the PUF. In this paper, we analyse the EM leakage of an RO-PUF implemented on FPGA, highlight its main vulnerabilities, and propose alternative countermeasures and architectures to mitigate the threat of this type of attack. Furthermore, we evaluate the cost in terms of area overhead of the proposed implementations compared to the original design.