$\Diamond(\omega_1)$ was introduced by Jensen and is known to imply $\mathsf{CH}$ and the existence of a Souslin tree. It is the statement that there is a sequence (in particular a $\Diamond$-sequence) of subsets $S_{\alpha}\subseteq\alpha$ for $\alpha<\omega_1$, for which given an $A\subseteq\omega_1$, the set $\{\alpha:A\cap\alpha=S_{\alpha}\}$ is stationary.
It can be interpreted as the statement that any subset of $\omega_1$ can be approximated arbitrarily closely by elements of the $\Diamond$-sequence. In this sense, it is called a guessing principle.
What I am wondering is if there are any guessing principles which guess well-orders. In particular, I am seeking a principle which given a subset $A$ of say $\omega_1$, which guesses a well-order on $A$. Are there such principles? If so, what is their current status in the hierarchy of various set theoretic principles? Links are appreciated.