If you work with protein sequences you can reach out to more distant orthology relationships.
In my experience, using HMMER's
jackhmmer tool to search for homology of a query protein against a set of target proteins is the approach that gives the most distant relations.
BLAST+ is a very good option in terms of speed/sensitivity if you proteomes are not extremely distant. OrthoMCL is a good option for simplicity of use.
If the two proteomes or sets of cdnas are close like human-chimp, it is important to be able to separate one-to-one from one-to-many from many-to-many orthologues, and for that using gene trees usually helps. There was a recent method published that is specially important for the analysis of gene trees for closely related species, called DLCoal: