Whispering excludes voicing from the linguistic inventory. Quite naturally, the decrease of the ability to comprehend a whispered speech depends on the language's original set of phonetic tools. Marc Ettlinger, linguistics PhD at Berkeley, shows that languages that intensively use voicedness and lexical tones are the most difficult to whisper in (from the point of the listener, not the speaker).
Replacing the Tools
(1) the laryngeal sphincter mechanism is found to be a principal contributing
physiological maneuver in the production of whisper, emphasizing the vertical rather than the horizontal component of the laryngeal source; (2) male speakers tend to lengthen vocalic duration and female speakers tend to exaggerate the amplitude contours of Tone 3 and Tone 4; (3) these two special behavioral maneuvers and two temporal envelope parameters contribute to tone recognition in whisper, but the phonetic context is shown to be a distraction; […]
Other works come to the different conclusion. For example,
This paper reports our initial findings on whether Mandarin Chinese has developed effective strategies to convey tonal information in whispered speech. […]
Results showed that, once turned into amplitude-modulated noise, originally phonated and whispered speech had similar perceptual patterns, and that these patterns resembled those of whispered tones. The acoustic analysis showed that properties corresponding to tonal contrasts in whispered speech already existed in the phonated tones, and there was no evidence of enhancement of these properties in whispering. Overall, therefore, Mandarin may not have developed highly special strategies to enhance tonal contrast in whispered speech.
A Practical Example
ASMR is one technique that intensively use whispering to achieve relaxation and positive feelings.
There are ASMR/whisper videos available in languages with lexical tone, like Thai and Chinese.
Please take a look at the latter one. The host gives Chinese names to people, and all these names are listed in the description below the video, providing with an easy-to-read transcription.
Although the lexical tone is inaudible when whispering, it is still possible to grasp the tone, even for a non-native speaker. As far as I perceived it, she indeed exaggerates the duration of Tone 3 plus she intensively uses facial expression and mimic (this, however, can be a part of ASMR technique).
The last, but not the least, context is everything. Many languages have homonyms, and speakers pick the right one by excluding words that don't belong to the context of the discussion or speech. Similarly, the whispered speech introduces more "pseudo-homonyms", but many of them can be safely skipped knowing the context.