A semigroup \(S\) with a unary operation \(*\colon S\to S\) satisfying the identities \((x^*)^*=x\) and \((xy)^*=y^*x^*\) is called a *-semigroup. A *-semigroup \(S\) is a regular *-semigroup if also the identity \(x=xx^*x\) holds on \(S\). The symbol \(\Lambda^*(S)\) denotes the lattice of all *-congruences on a regular *-semigroup \(S\). An idempotent \(e\) of a *-semigroup is called a projection if \(e^*=e\). First, the authors introduce a congruence \(\Theta\) on \(\Lambda^*(S)\) such that each \(\Theta\)-class is a complete sublattice of \(\Lambda^*(S)\) by: \((\rho,\sigma)\in\Theta\) iff \(\rho\) and \(\sigma\) induce the same partition of the projections of \(S\). Then the largest *-congruence of each \(\Theta\)-class and the largest projection separating *-congruence on a regular *-semigroup \(S\) are described. Further, if \((\rho,\sigma)\in\Theta\), the projection kernel normal systems of \(\rho\vee\sigma\) and \(\rho\wedge\sigma\) are characterized in terms of the projection kernel normal systems of \(\rho\) and \(\sigma\).