Considering a nontrivial probability measure \(\mu\) defined on the unit circle \(\mathbb{T}=\{ e^{i \theta } \, : \, 0 \leq \theta \leq 2 \pi \} \) and the corresponding orthonormal polynomial sequence \(\{\phi_{n} (z) \}_{n \geq 0} \), the authors review the notion of para-orthogonal polynomials on the unit circle and recall some features of the Christoffel-Darboux kernel \[ K_{n}( \varpi , z )=\displaystyle \sum_{j=0}^{n} \overline{ \phi_{j}\left( \varpi \right)} \phi_{j}(z)\, , \, \quad n \geq 0. \] Departing from important results of C. F. Bracciali et al. [Math. Comput. 85, No. 300, 1837–1859 (2016; Zbl 1336.42017)], K. Castillo et al. [J. Approx. Theory 184, 146–162 (2014; Zbl 1291.42021)], M. S. Costa et al. [J. Approx. Theory 173, 14–32 (2013; Zbl 1282.33017)] and D. K. Dimitrov and A. S. Ranga [Math. Nachr. 286, No. 17–18, 1778–1791 (2013; Zbl 1290.33008)], namely the following recurrence relation defined by real sequences \(\{c_{n}\}_{n \geq 1}\) and \(\{d_{n+1}\}_{n \geq 1}\), where \(\{d_{n+1}\}_{n \geq 1}\) is a positive chain sequence, \[ R_{n+1}(z)= [( 1+ic_{n+1})z+ ( 1-ic_{n+1}) ]R_{n}(z)-4d_{n+1}zR_{n-1}(z)\,,\;\;n \geq 0\,, \] \(R_{-1}(z)=0\,,\,\; R_{0}(z)=1,\)
which is fulfilled by a normalized \(K_{n}(1,z )\), this contribution aims to provide bounds for the extreme zeros of \(R_{n}\) in connection with the support of the measure. Several examples are developed in order to adequately convey the specifics of the given bounds.