We show that each set of n ⩾ 2 points in the plane in general position has a straight-line matching with at least ( 5 n + 1 ) / 27 edges whose segments form a connected set, and such a matching can be computed in O ( n log ⁡ n ) time. As an upper bound, we show that for some planar point sets in general position the largest matching whose segments form a connected set has ⌈ n − 1 3 ⌉ edges. We also consider a colored version, where each edge of the matching should connect points with different colors.