diff --git a/src/serialization/sb2.js b/src/serialization/sb2.js
index 7b6defd1d..affdc2868 100644
--- a/src/serialization/sb2.js
+++ b/src/serialization/sb2.js
@@ -12,6 +12,7 @@ const Color = require('../util/color');
 const log = require('../util/log');
 const uid = require('../util/uid');
 const StringUtil = require('../util/string-util');
+const MathUtil = require('../util/math-util');
 const specMap = require('./sb2_specmap');
 const Comment = require('../engine/comment');
 const Variable = require('../engine/variable');
@@ -642,7 +643,10 @@ const parseScratchObject = function (object, runtime, extensions, topLevel, zip)
         target.visible = object.visible;
     }
     if (object.hasOwnProperty('currentCostumeIndex')) {
-        target.currentCostume = Math.round(object.currentCostumeIndex);
+        // Current costume index can sometimes be a floating
+        // point number, use Math.floor to come up with an appropriate index
+        // and clamp it to the actual number of costumes the object has for good measure.
+        target.currentCostume = MathUtil.clamp(Math.floor(object.currentCostumeIndex), 0, object.costumes.length - 1);
     }
     if (object.hasOwnProperty('rotationStyle')) {
         if (object.rotationStyle === 'none') {
diff --git a/src/serialization/sb3.js b/src/serialization/sb3.js
index bcea2c702..254257069 100644
--- a/src/serialization/sb3.js
+++ b/src/serialization/sb3.js
@@ -447,6 +447,13 @@ const serializeTarget = function (target, extensions) {
     obj.broadcasts = vars.broadcasts;
     [obj.blocks, targetExtensions] = serializeBlocks(target.blocks);
     obj.comments = serializeComments(target.comments);
+
+    // TODO remove this check/patch when (#1901) is fixed
+    if (target.currentCostume < 0 || target.currentCostume >= target.costumes.length) {
+        log.warn(`currentCostume property for target ${target.name} is out of range`);
+        target.currentCostume = MathUtil.clamp(target.currentCostume, 0, target.costumes.length - 1);
+    }
+
     obj.currentCostume = target.currentCostume;
     obj.costumes = target.costumes.map(serializeCostume);
     obj.sounds = target.sounds.map(serializeSound);
@@ -1007,7 +1014,7 @@ const parseScratchObject = function (object, runtime, extensions, zip) {
         target.visible = object.visible;
     }
     if (object.hasOwnProperty('currentCostume')) {
-        target.currentCostume = object.currentCostume;
+        target.currentCostume = MathUtil.clamp(object.currentCostume, 0, object.costumes.length - 1);
     }
     if (object.hasOwnProperty('rotationStyle')) {
         target.rotationStyle = object.rotationStyle;