Consider the classical problem in enumerative geometry of counting rational plane curves through a fixed configuration of points. The problem may be considered over any base field and the point conditions might be scheme theoretic points. Recently, Kass--Levine--Solomon--Wickelgren have used techniques from \(\mathbb{A}^1\)-homotopy theory to define an enumerative invariant for this problem which is defined over a large class of possible base fields. This new theory generalizes Gromov-Witten invariants (base field = complex numbers) and Welschinger invariants (base field = real numbers) simultaneously. In this talk I will report on work in progress which explores the tropical approach to computing these new invariants. More specifically, for point conditions which are defined over (at most) quadratic extensions of the base field, we are developing a tropical correspondence theorem which expresses the KLSW-invariant as a tropical count. This result generalizes earlier correspondence theorems by Mikhalkin and Shustin and allows us to effectively compute some quadratically enriched invariants which were not known before. This is joint work in progress with Andrès Jaramillo-Puentes, Hannah Markwig, and Sabrina Pauli.