The sum of the degree-based topological index and its reciprocal index of a graph \(G\) is defined as \[TI_f(G)+RTI_f(G)=\sum_{uv\in E(G)} f(d(u),d(v))+\sum_{uv\in E(G)} \frac{1}{f(d(u),d(v))},\] where \(f(x,y)=f(y,x)\) is a symmetric real-valued function. In this paper, for the first Zagreb index (\(f(x,y)=x+y\)), the forgotten index (\(f(x,y)=x^2+y^2\)), and the Sombor index \(f(x,y)=\sqrt{x^2+y^2}\)), we establish the sharp upper bounds of \(TI_f(G)+RTI_f(G)\) for trees with fixed order \(n\) and matching number \(m\), and characterize the corresponding extremal graphs. These results extend the results on trees obtained by Gao [W. Gao, MATCH Commun. Math. Comput. Chem. 93 (2025) 535-547].