To clarify, can you not see the emojis in the source when you paste them in, or do you see them, but it gets garbled on saving?
If you cannot see them, this could be caused by a font problem – can you check what the text font is under General > Appearance > Colors and Fonts? Look for the Text font value under Basic.
If you’re seeing a character set warning when saving the file, can you open the properties of your Java file and check the encoding for the file mentioned in the Text file encoding block on the Resource property page? This may be different from your workspace settings for a variety of reasons.
Do send us a screenshot of your editor with an emoji in as well.