Effective population size (Ne) is a pivotal evolutionary parameter with crucial implications in conservation practice and policy. Genetic methods to estimate Ne have been preferred over demographic methods because they rely on genetic data rather than time‐consuming ecological monitoring. Methods based on linkage disequilibrium (LD), in particular, have become popular in conservation as they require a single sampling and provide estimates that refer to recent generations. A software program based on the LD method, GONE, looks particularly promising to estimate contemporary and recent‐historical Ne (up to 200 generations in the past). Genomic datasets from non‐model species, especially plants, may present some constraints to the use of GONE, as linkage maps and reference genomes are seldom available, and SNP genotyping is usually based on reduced‐representation methods. In this study, we use empirical datasets from four plant species to explore the limitations of plant genomic datasets when estimating Ne using the algorithm implemented in GONE, in addition to exploring some typical biological limitations that may affect Ne estimation using the LD method, such as the occurrence of population structure. We show how accuracy and precision of Ne estimates potentially change with the following factors: occurrence of missing data, limited number of SNPs/individuals sampled, and lack of information about the location of SNPs on chromosomes, with the latter producing a significant bias, previously unexplored with empirical data. We finally compare the Ne estimates obtained with GONE for the last generations with the contemporary Ne estimates obtained with the programs currentNe and NeEstimator.